I vote for 3.90's manual. I've had the 3.08's originally and 3.73's for a while and I always wonder what that bit more would be like. It's like free power (if you opt for the 3.90's over the 3.73's at time of install).
However, I do think that you may be pushing the $300 a bit. Gears are $175. Realistically, you are gonna need a bearing & install kit, too ($100). Speedo gear(s) ($20). Lube ($?). Permatex ($4). Cleaner for the housing ($10). Axle bearings (good idea, not necessarily needed $25). A posi rebuild kit would also be nice ($50) as yours, unless newer, is probably toast. All this considers that you are doing this yourself and have the tools. Add labor, and I don't honestly think that you are going to get it done for $300. BUT... it is still worth it, regardless if it costs more. I'd just save until you can afford gears rather than spending it on something else IF you want the most performance bang for your buck.
BUT there are plenty of other good choices for upgrades if you aren't necessarily looking for the most performance for your money. If not, I then say catback. The sound is worth it.
Shifter is a good choice. If I was adding a shifter and had $100 to spend, I'd probably save for gears.
Gears rule. ANYWAY I'd spend that $100 on subframe connectors. Really stiffens the car up. But, then I do like good handling. If you don't care that much about cornering, then there are other good choices.
Like a nice stereo if yours is ghetto. Gotta have good tunes.
What I'm getting at is that comes down to what's important to you. Without specifiying I have to assume performance. Telling us that will get you better targeted responses.
There are just too many cool mods in that price range that it's hard to decide!
Rick
(all prices approximate and just from my reccolection)