The TOYO RA-1 is DOT approved and therefore is legal for the street. Especially that it has more tread than the Kuhmo 700 and 70A. Obviously, when they get used up and have minimale tread, you will have a hard time convincing the constabulary forces that it is okay to use them in the rain. If you are looking for a long lasting, sticking, predictable track tire, then the RA1 is the tire you have been looking for. The TOYO T1-S is an excellent street tire that shines in thunderstorms, which is why several racers will use it as a full rain tire. But as a track tire, it is not at par with the RA1. If you want even stickier, then you could go with the Kuhmo Victoracer V700. Its newer cousin, the V70A, is not as good. Hankook has the new Z211 which is supposedly a nice comprimes between the RA1 and the V700: long lasting, predictable and very sticky. But have not tested it yet. Then when you are a champion, you can go with Hoosiers, but they will last one set for two weekends.
If you are only starting lapping or driver school, then stick to your usual street tires. They are less sticky and might even get greasy when pushed hard as the rubber was not intended to reach the same temperatures, but at least you will learn more with slippery tires.