I've used a TI-83 Plus since I was a sophomore in high school and it hasn't failed me yet. I think the TI-84 is just the upgrade from the 83, I think the 84 has a USB port to connect it with a computer. It would be a nice feature to have, but maybe not necessary for what you're going to do with it. I wouldn't go higher than the 84. I have a friend who has a TI-86 and can't figure out how half of the thing works. With the 83 Plus I could do all of my calc and chem calculations and even make programs with useful information in them. It does take some time to get used to how the commands operate if you've never had a graphing calc before. I would probably go with the 83 Plus because its a little cheaper I would guess. And you can always get awesome games for your calculator like PacMan and Duckhunt 👍
I would go with a TI-89. Heyitscyndi has made a good recommendation too. All my professors use the TI-89 It's a more advance calculator, but the TI-83+ can get you pass chemistry and pre-calc. All my professors use the TI-89 and recommend it. It's a really solid investment if you plan to go into calc or stats IMO.
I LOVE the ti-89 and would probably die without it. Gotta love pretty print. Just make sure you don't use the solver functions unless you're checking yourself, otherwise you'll probably end up not learning the material.