TXSpeedDemon

I've put pretty close to $10K in my car - sort of the way you are describing without any cheesy stuff. If I had all that money to spend at once (or was patient enough to wait 4 years to do it) I would have gone with a turbo or SC kit without any doubt. NO DOUBT AT ALL. I like my mods and the car, but with that kind of immediate cash it's best spent on forced induction so you really feel like you got something out of the car.

That being said, if you don't want to do forced induction here's what I would recommend.

Lighter wheels and tires. If you get something really nice this could eat up half your budget. But, if you can manage to reduce +5lbs off each corner you'll feel the difference in acceleration and handling. I dropped 7lbs off each of mine and it was definitely apparent. If you don't want to go with new tires you could simply replace the wheels with something lighter at the same size and width. Or go slightly wider and have the stock tires be stretched on the new wheels till they wear out and replace them with wider tires.

Swaybars, springs and stronger endlinks. Car will handle better than ever.

Intake and exhaust. I'd look for these used since most of it is hidden from view 95% of the time. Doesn't have to look perfect, just work.

A Tune - either uprev or custom.

Upgraded sound. I would suggest the Wicked box that drops into the spare tire. I have a z enclosure box which eats up about 45% of my usable trunk space and with my 2 subs weighs in at about an extra 100lbs.

If you have any money left I'd go for lighter brake rotors. I haven't been able to find weights listed for any of the major brands (just the one vendor on here selling them for $1K a set) but shaving some more unsprung weight off the axels will increase horsepower, response, braking and cornering.
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Here's what I bought.
Greddy TiC exhaust ($1300): I'd recommend this if you don't want something too loud. This sounds AWESOME with the silencers in, but ungodly loud with them out. There are others that get better gains, but this is good enough. Plus it's 2.75" true dual so no need to upgrade when going Forced Induction later unless you're running really high boost levels.
Berk Hi Flow Cats ($200) used
Stillen G3 Intake ($250) used

19" Volk TE37SLs ($3600)
Michelin Pilot Super Sport Tires ($1200ish)
These were the best additions to the car. Only thing where I felt a power upgrade.

Hotchkis Sway Bars ($350?) - don't remember how much these cost. I like them but a lot of other options are now available. These were the only ones out when I bought them in 09
SPC rear toe/camber arms ($150)
SPL Endlinks ($185)
H&R Lowering Springs ($225)
This combo changed the feel of the car a lot. On the stiffest setting the car is pretty tight, but rotates through the turns quite well. With the lowering spring I can't drive over a coke can.

Eclipse DVD deck, Infinity Kappa Perfect component speakers, 2 boston Acoustic G5 10" subs, 2 boston acoustic amps, lots of sound deadening and dynamat (about $2K). Having 2 subs is WAY overkill. One 12" sub would be better and like I said earlier I would have gone with a lighter sub and box combo. I plan to redo all this next year since my stereo seems to be fading out after 4 years now.

All total about $9,500 over the last 4 years. Like I said I really like the car, but if I had all the cash at once I would have gone forced induction without a doubt. Mods like these make the car nicer, and more unique... but forced induction makes the car a whole different car and more unique than any other combo of smaller mods. Unless you really are happy with just a "quick" car that looks good and don't want a fast car that looks good I would recommend (from my own experience) you invest that money in forced induction.