Problems...your not going to be making that much power with an N/A 3800.
I'd say more along the lines of 200-225. Maybe with...
Some sort of intake
Ported/Polished UIM
Ported/Polished LIM & Runners
Ported/Polished Heads (I'd mill the heads/block and get custom length pushrods to bump up compression even more)w/ Crow 105's/Titanium Retainers
GT2 Cam (From ZZP)
Long Tube headers/exhaust of your choice
Larger Throttle body of sorts...not sure what FBody guys use...
GTP Injectors? If need be.
HP Tuners...that thing will need some lovin' after a build like that.
Gear wise? I'd rock a 3.73 Rear...keep in you in the powerband and not be a killer on gas. If you don't care about that...then how about a Ford 9" with a 4.10? I think that is what my buddy has on his '02 SS.