To make things easier for you, search the forums and you'll find the most popular tires (depending on the diameter) are Dunlop Direzza Star Specs ZIIs, BFG Rivals, and Falken Azenis RT615K. Lots of teams use other tires and some might be better than others or offer equivalent perf for less money/tire (just google your potential cnadidate) but generally people are happy with all three of the above choices.
As far as spare tires are concerned, if you buy these tires, you will want to use them as your "primary" set. You could probably get away with keeping your other used tires as "race spares" (we did on our first race) and then the next time you decide to buy new tires, the primary set becomes your spares and your original stock ones get sold off.
This all assumes you keep the same diameter with your spare set as what's currently on the car. You could mix-match tire sizes/diameters but in the event you blow a tire, you'll have to replace them in pairs and handling will likely change.
Myopic Motorsport's #888 Bosozoku Texino Thunderbird (1995 tbird w/ 93 V8 swap + shopping cart rear wing)