I have a 89 Firebird Formula with the 5.0 engine, th700r4 tranny. 10 bolt rear end. My rear end is making a terrible grinding noise and was told i have a carrier bearing going out. I quit driving it last year and am now looking to rebuild the rear end. I am planning on doing the rebuild myself, replacing all the bearings and putting a new posi carrier with 3.42 gears and upgrading the axle shafts from the original 26 spline to 28 spline shafts. My question is, when i buy the new posi unit is it the 7.5 or the 7.625 posi unit? I have been looking on Sumit and I am not sure what to get. What brand is the best to get?

You can put a 7.5" gear on a 7.625" posi and vice versa. The thing is the spline counts. With genuine, used GM units, the diffs changed the "windows" for installing the spiders and such, so the early 7.5" 26 spline used 2 symmetrical windows, then for '85-up they went to one small window and one large window. This only matters if you are buying a PowerTrax or some other such conversion-style locker.
The Eaton is a good choice, I prefer the Auburn, even though it is non-rebuildable, while the Eaton is rebuildable. You might find a good used torsen on LS1tech.com, torsens don't wear out, and smart guys sell them before breaking them.

I think the Eaton Posi is the best. Get it with 28 spline axle gears to match the axles. Be sure that you get a good installation kit with Timken bearings. Do you know how to set the pinion depth, bearing preload and backlash to get the correct contact pattern?

No i dont know how to do this. I have been trying to do as much research as i can so i do this right. A lot have people have been telling me to get it profesionaly done but around where i live it costs way too much money.

Randy's sells a tool, that noone else offers, to help with this, and Richmond Gear makes a good video you should watch before ordering anything.