My first mod was a flowmaster muffler. I only got the muffler 'cause I couldn't afford an entire exhaust, so if you can afford the whole thing, go for it. If you're new at stick, I'd hold off on this until you get better at it. With a louder exhaust everyone can hear your mistakes.
My second (and favorite) mod was the TRD rear sway bar. The car corners much flatter and there's much less understeer. In fact, I've even gotten the back to step out. They're discontinued, but they pop up for sale on here occasionally. This is where I got mine.
My third (and easiest to install) mod was an injen short ram air intake. The stock airbox is great for quietness, but it's really restrictive. Your car will breath much more easily with the SRI, and it sounds great too. I've since added a cold air extension to it, but the SRI alone is a great improvement.
I have an auto, so I wouldn't know about the short shifters available for the solara. Search around, theres a wealth of information here.
Those three mods correct what I think are the solara's biggest flaws.