The online tire/wheel sites are pretty decent regarding fitment. I just got 7x18 inch gold rims for my '03 SLE w/the gold package and they look awesome.
7 in. wide by 18 in. in diameter is as big as I would want to go. There's enough wheel well room to go completely wild and go with 22 in., but I doubt anyone here would recommend that.
I would go with an 18" wheel and tire package that you can afford. It will cost another $50 to $70 bucks to have your old tires removed and taken off the rims and disposed of - if that's what you choose to do - and have the new rims and tires put on. The online stores will balance the tires on the new rims before they ship them. I've done this to two cars and had a good experience both times.
The biggest hassle was having to get a couple spacers from a local wheel shop for the rear wheels on the Solara because one of the rims rubbed the right strut just ever so slightly to make a noise. It was no big deal and the spacers worked out great.
Do your research and shop around for the best deal on the rims you like. Most of the online stores make you enter your vehicle info so they know what size rims and tire package will fit your particular car.
I would also consider lowering your Solara by investing in adjustable coil-overs that replace your existing shocks. Coil-overs are shock/spring combinations that replace the existing shocks/struts and springs. They improve the stance of the car by making it look more aggressive and improve the handling, though the ride will be slightly rougher than the stock suspension provides. I find the stock setup very soft and mushy and can't wait to upgrade and lower the suspension on my '03.
You might also want to look into getting an INJEN air intake to replace the stock air box and replacing the stock exhaust with a high-flo 2.5 inch cat-back exhaust. These will increase HP and fuel efficiency (unless you have a lead foot) by letting the engine breath easier. Plus they make the car sound totally sweet. If you're into that sort of thing.
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