for supporters and esp. critics of the Bible
Hopefully, all with strongly-held views on the Bible (whether supportive or critical) have gotten those through careful study and reading at least somewhat from those who are supportive and critical of it.
While reading the whole Bible would be quite a load, one would expect a critic to have read a good chunk of it that was representative and/or crucial to its themes and claims. (It's safe to assume that any critics reading this have more dignity and intellectual honesty than to rely solely on snippets, snark, and/or what critics have said about it.)
I think it'd also be appropriate to expect that one would revisit the Bible once in awhile-- say, every 5-10 years. As we change/grow, then our encounters with great, provocative literature can vary significantly. It'd be a shame to criticize that which I would now embrace or respect-- if I were open to giving it a new/fresh reading.
If you haven't read a big chunk, then I'd recommend Genesis and the New Testament.
If it's been awhile and you're looking for a refresher (particularly if you have not already read some of these at all), I'd recommend some of the following:
-Genesis 37-50-- the story of Jacob's family, esp. Judah and his more famous brother, Joseph. Leon Kass taught (still teaches?) a "Great Books" course on Genesis at U. of Chicago for 30 years. He turned the resulting discussions into a marvelous 800-page commentary, The Beginning of Wisdom.
-Ecclesiastes and a handful of Psalms-- e.g., Psalm 2, 22, 23, 42, 51
-Some of the prophets--e.g., Hosea 1-3, Ezekiel 16:1-6 (and read on to vs. 49-50 if you want to see the Bible's definition of "the sin of Sodom"), Isaiah 52-55, Haggai, Malachi
-The gospels of Luke and John
-The book of Romans
-Revelation, especially if you tend toward the more artistic or poetic side of things