There's so much content, even if you don't play BL3, you'll have a lot of fun! BL1 and BL2 have a GOTY edition with all the DLC (from memory, between 4 and 6 story DLCs per game, BL2 also has 2 additional characters and a sort of max lvl / extra difficulty mode), and are super cheap at this point. Do wait for a sale if possible, BL1 GOTY Enhanced is frequently 67% off ($10), and BL2 GOTY 80% off ($9)

There's also The Pre-Sequel, which came out after BL2 and plays between BL1 and BL2. Gameplay is like BL2 with some additions, but it's not as good as BL2. Still worth playing imo, but the community is split on it. If you play it, even though it plays between BL1 and BL2, it's intended to be played after BL2.

A lot of the more interesting things regarding character builds & weapons happens in NG+ and NG++, you can spend ages just replaying it and farming bosses & chests in the endgame, and the coop is also really nice (but not at all required). I definitely recommend starting with the first one, and if you do, I think Lilith has by far the most interesting gameplay. In BL2, I think almost every character has fun gameplay, just Axton feels a bit boring to me personally.