For the V6 Solara, the supercharger is the popular way to get more power. As others have said, swapping the pulley is common too - 6 lb pulleys seem to be the highest you can "safely" go without having to do a ton of engine work. The supercharger seems to go retail for about $3500 - look close to $4000 USD after shipping and install and such, if you go retail and let someone do it for you (and if you're not a gearhead, I'd suggest that). I've seen people swap out their injectors for ones from the Supra, but I'm not sure how that is done, how much it would run, or how big of a benefit you'll get.
If you're not looking to go that far yet, maybe a short ram intake would benefit you. It's not a huge difference, but it will be noticed. I'm using a K&N High-Flow air filter instead of the stock paper filter; it's guaranteed for something like a million miles and all you have to do is rinse it out and oil the edges. It gives you better air flow, which improves gas mileage - and it sounds pretty cool, too!
For body kits, you're okay because you have a 99-01. The body kits don't need to be modified like they do for the 02-03, so if you find a good one from a reputable source it should be close to bolt-on. There's lots of them out there, but the most common is the Tracer kit (check eBay) and also the Molly Designs kit (which I hear they no longer make - good luck!). For wheels, the biggest I've seen be used "easily" (that is, without having to work on the car a lot to avoid rubbing) is 18" with low-profile tires. Lowering the car is fairly common too, and can be done with lowering springs. Be sure to change out your shocks for stronger ones, as lowering the car on stock shocks can blow the shock within a year.
If you feel like being seen, HID conversions are fairly common as well. The kits, as far as I've seen, go for somewhere around the $200-300 range, and can be done by a willing and patient Solara Guy in the course of a Saturday afternoon. You'll get unparalleled lighting out of it - but if you're not willing to spend that much, Silverstar headlights are nice as well, and you can swap out the headlights, foglights and even the turn signals (check my www if you want to see mine, or go to the Pictures and Videos forum and check the "Silverstars Shinin' In The Night" thread). As a sidenote, the 9005 bulbs are brighter than the 9006 ones (the 9006 has a silver coating that covers the tip of the bulb, the 9005 does not). The 9005 can be modified to fit the 9006 socket if you take a knife or dremel to the plastic prong inside the plug part of the bulb - do that, sand it down smooth, and put one of the plastic o-rings from your old bulb in with the other one on the 9005 to give it a better seal (I've seen it work without the extra ring though), and you're good to go. As with any bulbs, don't touch the bulb with your hands - I have a shop towel I keep around for changing bulbs. If you handle them carefully, and don't have weird tripped-out wiring, the Silverstars can last you just as long as normal bulbs (don't listen to the nay-sayers who say they burn out easy).
You'll find clear corner-light units on eBay for $15, use them at your own risk as sometimes they don't fit right. If you want to remove the amber relfector yourself, it can be done with some patience and an oven - check out the Tutorials forum, there's an awesome turorial there for doing this. You'll also find altezza-style tail lights, in chrome and carbon fiber, on eBay. I've also seen some people getting the headlights smoked, but I don't know much about that one.
There's dash applique kits to add to the accents in the car (be it wood, carbon fiber, brushed aluminum or whatever), you can go with those if you want. Also, check out the forums when you get bored and just browse the pages to see what you find - the Pictures and Videos forum is good for that, as are the Tutorials and the Aftermarket Upgrades forums. Just read up, and if you want to find something, the Search function actually works pretty well. Just remember that if you don't feel comfortable doing something, check for a tutorial or ask around - and if you still don't think you can do it, don't. It's not worth "experimenting" and doing something really bad (and expensive to repair) to the car.
Welcome to the Solara family, too.

(Yeah, I've been doing my reading up on stuff to do to the Solara too!)