Is this a place for competitive karting? Also how can I sign up to race competitively here? How much does it cost and do you need to bring your own race gear? (go kart, helmet, gloves,

Depends on what you mean by competitive, but in short, yes. If you do the CalSpeed hosted sport kart series, they can provide some gear, but it's recommended to invest in your own helmet (remember, you're investing some safety for your head). You get to rent a kart throughout the day and compete against others. If you want something more serious, some clubs that race here are Tri-C Karters & Los Angeles Karting Championship (LAKC). Both are much more competitive, and you would need a different type of go kart than the sport karts called a sprint kart. However, some of the teams here provide some rentals throughout the day for some of the entry level classes. You would need your own race suit, helmet and gloves. I recommend showing up during a race to just watch, ask questions and learn what to expect with some of the basics (meeting weight for your class, understanding the different classes, learning the track layouts, etc.). It's a big price to get started, so do your homework.

Yes it is a competitive racing circuit. They have a school and a racing series. They have all the gear if you are renting their karts. http://calspeedkarting.com/rental-information/