ASP is still a street car class (street prepared), just look at the SM and Mod cars. In AS classes are your limited to certain engine mods and weight reduction. But yes, suspension is pretty much what you want so you will get guys with Motons and such in the SP class (typically, they are the dominant guys). The name is very deceiving as it implies a budget racing class but it's not, neither is the ST classes which where originally intended to be that. SM is pretty much anything goes as long as the car is street legal (debatable). Mod cars are full on cage space frame specialty racers.

Keep in mind that even "stock" classes allow some mods (1 way adjustable shocks etc...) and R comp tires are allowed in all but the ST (Street Tire) class. Even then, the approved street tires rival some of the lessor R comps in performance. In the SCCA money is the name of the game if you want to run at the top of the pack. Plus the participants tend to be very competitive in their nature and are not welcoming and not very newbie friendly. They expect you to know the flow and procedures almost off the bat. I had to learn everything the hard way. They only want to know about your car to see if there is anything they can protest to disqualify you (in the event you win). And yes this has happened to me in the past. Not much camaraderie and in general car enthusiasm. Yes there are some people that are cool but not the rule of thumb there.

I put up with it for a few years and grew tired of the whole atmosphere. I still autocross but not with them obviously.

/soapbox