Honestly...how far do you want to the go with the car? If your mechanically inclined and have deep pockets you can go well into the 13's N/A...its just a sh1t ton of work. Hell, if you got the transmission for it...you can toss the bottle on it and run 12's.
I'd set her up like this...
Fenderwell Intake of some sort...make one
180* T-Stat
Autolite 606 Spark Plugs
New Wires (Upgraded or stock...doesn't really matter, but PRJ wires are *****in)
Speed Daddy Catless Headers (Your '04+ anyways...so your car doesn't have a U-Bend from the factory...and use the stock catback...you'll thank us)
ZZP HV3 Upper Insert
HP Tuners...you'll need the pro version to tune your car just fine...or take it to somewhere close to you to have it professionally done or someone that knows their way around the 3800 platform...plus, it isn't too hard to tune a N/A car
Yank off your throttle body...and clean it. Then get some 1500/2000 grit sandpaper and a flapper wheel...and polish the inlet and outlet. Worked well on my DBW TB 2.2 Cobalt...since there aren't TB upgrades for the '04+ 3800.
TransGo Shift Kit...get one from Triple Edge Performance
Poly Mounts...get 'em from ZZP...the upper ones. Then, get new solid rubber lower engine/trans mount
As far as it sits now...that's a 14's car if you can drive.
Then...it's either cam or rockers...both...get upgraded valve springs...Crow Cams 105's w/ Retainers...and either get 1.95:1 Roller Rockers from Intense or ZZP...or get a GT1/GT2 Cam from ZZP. With head work on top of that...I don't see how 13's would be out of the question if you were driving it right and it was tuned to its full potential...
OP says he doesn't want boost. Therefore...kinda like beatin' a dead horse
LOL