If you are gonna run it at the track go with a set of P225/60/R15 "V" speed rated tires. This size was original equipment on 5.0L Mustang GT's & LX's back in the day. You can find this size in plentiful variety. The V speed rating gives the tire a stiffer sidewall and in case it brakes loose on ya at the track it could possibly save your life. When I worked for Goodyear in the early 1990's we used to sell The Eagle VRS in that size which was a soft compound competition tire used for oval track racing. It was meant for Mustangs but some guys with early 3rd Gen Camaro's used it to.
You can go with a P225/60VR15 on a 15x7 wheel up front. On the back some drag radials with a a 15x8 will work just fine. The P225/60/R15 has an overall diameter of 25.62 and circumference of 80.48" in....
Whenever you are switching tire sizes up front it is best to keep the overall diameter the same. The problem is too many guys don't do this when using the +1 method on these cars. Lets use a 3rd gen for example: a P205/75/R14 on a Camaro Berlinetta has a 26.10 overall diameter. The plus one would be P215/65/R15 which is what the early 3rd gen Z28's came with and this overall diameter is 26.00....A P235/60R15 is 26.10.......Now on the 1990 5.7L IROC-Z's & Formula 350's, the tire size was P245/50/R16 which was 25.64" in OD...The SLP Firehawk in 1992 had P275/40ZR17's on it which were 25.66" in OD....FWIW that 17" size was also used on the front of the ZR1 Corvette.
The point is the overall diameter is critical if you are looking to minimize issues. But you should be ok. I know it's a first gen and not an IROC-Z...I've seen guys go with P215/65/R15 to P245/50R16 which is .36 difference in OD and not mess anything up...For you it would be .25" difference up front.
On the rear, drag radials should be just fine on a 15x8.....A P295/50/R15 has an OD of 26.61" and BFG makes a good tire in that size. If you can find a P305/50/R15 that would be 27.00" in OD which means your speedometer will be accurate as well. Hard to find it in a P305/50R15 though even back in the day as well....
Jegs & Summit sell drag radials and I think Jegs may have a wider selection. Good Luck with the selection and Happy Motoring!
P.S. It's been 11 years since I mounted & balanced tires but if memory serves me correctly I think the lug nuts are called acorn lugs and the standard Rally Lug nuts will work fine. Since you have mini-tubs you may be able to get a 15x8.5 Rally or 15x10 with and still be ok with an even larger tire like a P315/50/R15 or P325/50R15. P275/60/R15's will also work but the wider tire will increase your contact patch and help with dry traction on a hot summer day. Just my 2 cents on the topic. I hope this info helps!