Full treads if you are on a budget, both if you have the money.
Aren't the full treads slower though?
I would not really worry about the full treads being slower as seconds off of laps will not really be seen until you are consistently fast in your car. After 3 years of racing I can finally run consistent fast laps in my car, so for me the full treads are 2-3 seconds slower a lap (more at some tracks), for a beginning racer they will be fine and more cost effective as they will last longer and you will not need a set of rain tires just yet, the full treads work as rain tires too.
If you have the cash to spend, it is ideal to have multiple sets of wheels and tires. You will need at least two sets of wheels and tires when you get deep into racing, a set of shaved newer tires and a set of full tread rains, because sometimes it rains and we race in it, and it is absolutely impossible to race in the rain on shaved tires. I prefer to have three sets, one newer set of shaved tires, one older set of used shaved tires, and a set of rains. The older tires are faster on tracks that have been recently paved as the compound is harder from the age and heat cycles, and the newer grippy tires are faster on tracks with less traction like Sebring.