Normally I customize this a bit based on exactly where my audience is coming from, and sometimes what question was asked. For HN I guess I'll assume someone who is aware of the pop-culture version of Christianity (which honestly describes a lot of people who went to church as a kid), not an active Christian, dabbling a bit in philosophy, and capable of understanding big words.
(Technically, "The Bible" is plural meaning many books. But in English we usually treat it as a single book despite using "the book of X" for its componentse)
The Bible is not a novel, and it is a grave mistake to try to read it like one. The Bible is also not a textbook, though that's closer.
If we treat it as a philosophy book, I'd say the core theme would be "What is sin, what does that imply, and what can we do about it?", though this is often implicit, and much of the book is in the form of negative answers. I expect that if a reader doesn't ultimately "get" the mindset behind this question, the Bible will never make sense, never see it as anything more than arbitrary rules interspersed with random supernatural events. Yet, I also don't think approaching the Bible from this big-picture perspective is particularly useful - certainly, many people who read it are not into philosophy (as we now mean the word) at all.
Rather, the Bible is food. You need to eat it regularly or you'll starve, and you need to give it time to digest or you will expel it without it taking effect. Like food, you should have a variety; some parts are not meant to be taken alone, while a few favorite superfoods you could in fact survive on if you had to. Some parts are low-density and some are high-density.
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The "Sermon on the Mount" in chapters 5 through 7 of Matthew is some of the highest-density content in the Bible, and (orthogonally) is designed for immediate practical use. It's even possible to spend a whole week studying a single verse for some of it (and ~3 verses per week for the rest), though I do not recommend this for newcomers. Even if you are missing 99% of the point and have no idea what you are doing, you can still get something out of these chapters if you're taking them at a rate of one chapter per week.
A rate of one chapter per week is sustainable throughout the gospels and several other frequently-read books; for some other books, maybe 5 chapters per week is appropriate. Note however that chapter size varies quite a bit (~15 and ~50 are common) and chapters are not in the original (so if you're doing this alone, feel free to split or merge chapters even if the density is right, and consider verses from the adjacent chapters for context). For the "per week", at least in the high-density parts, I suggest reading the whole thing one day, then on later days focusing on a few verses that jumped out at you, and keep them in your thoughts as you go out for your daily life.
From Matthew 8 onward, the content density isn't as extreme but it's still pretty high, and by now you're starting to get your feet under you.
For a first read, I actually recommend finishing Matthew without ever going back to the first 4 chapters (not that you can't, I just don't have a good place for them), then reading Luke (which includes an even more extended start than Matthew has), Acts (the explicit sequel to Luke), and John (the gospel according to, not the epistles of) in that order. At one chapter per week, this will take about 2 years (note that part of the reason for this order is because some people might not think they want to commit to that). After this, start poking around well-known books or parts thereof (see below), then come back to do Mark. After this it's open season. At some point, learn to use margin references to discover new chapters to study.
As a rule, in any given year, you should spend half your time in the gospels (which is common but sloppy shorthand for "the gospel according to {Matthew,Mark,Luke,John}"; strictly speaking "gospel" refers to "this is Jesus, the accessible and reliable solution for sin"), though not necessarily going chapter-by-chapter like the first time. When you eventually start reading the more difficult or low-density-food books, I suggest alternating on a more frequent basis, like every other week. Or, quite possibly if you're still here, you might be doing two independent study lines the same week - perhaps one assigned for a group, the other chosen by you personally.
Some good books to consider reading, but only after Acts (and in my plan also John) include: Ruth, Jonah, the first half of Daniel, any of the short epistles (some specifically suggest James). There are also many scattered famous chapters in other books but I keep failing to make a list thereof. You will usually find references to these in the margin so don't be afraid to follow them (I'd suggest gradually ramping up how often you do this as you go through your second or third gospel), just don't get distracted from going through the gospels until you've finished them all at least once. Hebrews 11, however, is remembered for being a chapter that many of the margin references are made from.
Note that the Bible is in part sorted by similarity. As a result, it is often a bad idea to go from one book to the adjacent books. This is particularly notable for Kings/Chronicles (two retellings of the same events) and several of Paul's epistles (same advice written to different people), but also applies within the Psalms (and Proverbs/Ecclesiastes, but they're shorter).
Some books that can be a bit of a slog, and/or with little food content in parts, yet are somewhat reliant on sequencing: Genesis through Joshua, Ruth through Nehemiah, and the two epistles to the Corinthians (other numbered epistles are more independent). To be clear, there absolutely are even large portions therein that are both easy to read and profitable, but you should still approach them with deliberation.
Some books to avoid for a while: Judges (full of negative examples), Job (much dreary philosophy which is immediately rejected), arguably Ecclesiastes (but other people like it), Song of Songs/Solomon, all of the prophets except sometimes when excerpted (Isaiah in particular is commonly cited), arguably Romans (I personally don't find nearly as hard as Hebrews, but others disagree), Hebrews (but chapter 11 is very notable to read on its own), Revelation (so many people go insane after reading it, it's not even funny).
This is not the only way to read the Bible, and certainly there are other good ways, but I do have reasons for my particular choices especially for someone with no foundation.
All translations are biased. Some translations have their bias obvious (which is good) or aimed at a target that is no longer applicable (also good); others are subtly problematic.
Avoid, at all costs, any translation that goes nuts with paraphrasing (moderate paraphrasing is usually okay). Mostly this means The Message. Also avoid any translation that is only used by a single denomination; semi-related to this, I also suggest avoiding any "study Bible", which inevitably consists more of third-party ideas telling you want to think about the passage rather than just reading it for yourself. I have nothing, however, against mere narrow-margin cross-references and rare single-word translation notes.
Other than that, for the gospels it doesn't matter much. Outside the gospels the differences become much more apparent.
The KJV (sometimes KJB or AV) has been highly influential on the English language (and, per its preface, the translators were very aware it would be). If you can stand the "thee"s and "thou"s (which do add important pluralization meaning in some places) and archaic spellings, it remains of excellent quality in most passages - better, even, than many modern translations. Its biases mostly fail to take hold of a modern audience. However, it does measurably suffer from the lack of modern linguistic scholarship in some passages (mostly, idiom-like things in the Old Testament, especially Job/Psalms/Proverbs and the prophets). Traditional editions do lack the quotation marks and paragraph flow that modern translations tend to use (though basic paragraph marks are usually present). Note that what people actually use is usually the 1769 edition, not (as some only-ists claim, the "original" 1611 which is unreadable), though there are some minor variations (such as "graffed" vs "grafted").
If you want something that keeps the KJV's advantages but is more modern, the ASV is mostly obsolete, but the NKJV is recent and pretty common (at the cost of giving up on the pluralization disambiguations). The KJ21, though much rarer, is quite useful because it does preserve the pluralization but modernizes the rest of the wording.
The NIV is popular, but I actually find it quite problematic. I have caught it on several occasions flat-out making something up, far beyond what can be explained by being a moderate paraphrase or even preferring different manuscripts. In particular, if someone in a debate cites the NIV, they're probably wrong. I think I've only once found a verse where the NIV gave a useful reading where other translations did not.
The ESV is not bad. It has its (unavoidable) biases but they are mostly of the obvious sort despite being aimed at a modern audience. However, I have found a few places where it introduces errors and ambiguities not in the KJV, such as Luke 22:31-32 (rigor summary for this verse: KJV/KJ21/NRSV/NASB good, NKJV bad as usual, NIV good for once, ESV bad for once). It is also prone to the problem of there being different editions in the wild with non-obvious differences.
The NRSV and NASB also seem relatively widely regarded, though I'm less familiar with them despite using them as parallels. They do succeed at the Luke 22 rigor test, at least in the versions I happen to have accessible (unfortunately, like the ESV, they do have non-obvious version differences).
There are a handful of other decent translations not mentioned here. But there are also a lot of low-quality translations, as well as minor variants of existing translations.
The YLT (not the Mormon "Young") is obscure but useful if you don't know enough Greek/Hebrew to efficiently use an interlinear directly, because it goes all in on literal translation, even for verb tenses that are unconventional in English.
