S3 Pro's are a very common choice for track tire, both for training and weekly racing. I wouldn't necessarily take them to Manchester for Masters' Worlds, or to ADT for a World Cup event, because there are more supple and lighter tires for those events. But they are a lot better than the heavier S3 Lite's (195 and 215 gram) or the Road Elite's, they are consistently round and straight, and they don't cost a lot. They also have a bare base tape so you don't have to scrape the latex off like you do on some heavier training tires.
Alternatives? The big competitor in this range is the Conti Sprinter. It's not as consistent as the S3 Pro -- when it's even and straight it's dynamite and I stock up for use on concrete track racing and the like, but when it isn't it tends to annoy you a lot, especially with bumps and unexplained flats. The Sprinter sticks better on some steep wooden tracks. You should check around your local track (you didn't say which one it was) to see what tires stick and what ones don't. It isn't an issue on shallow tracks, or on concrete or asphalt ones, but on steep wood tracks it's a common discussion. A tire can work one one steep wooden track and not on another -- S3 Pro's sometimes slip at the ADT Center but do fine at Blaine, for example. Sprinters nearly always work -- they are relatively fat, the tread wraps around the tire well, and the rubber is black and adhesive -- all attributes of a good wood-track tire. Go look at Conti Sonderclasse's and you'll see what a superb steep wooden track tire is like.
The S3 Pro is a decent diameter (21 millimeters, more or less). You don't want to ride too narrow a tire except for major timed title events. It will last you a season assuming you don't ride over something really nasty. It has higher odds than for most tires of being straight and round, without bumps. And it actually is surprisingly supple. Absolutely nothing wrong with it for any training or racing use in your first couple years, as long as your track surface doesn't have problems with it. You'll have to inquire locally, or indicate which track you're riding.