Well, it really depends on your experience and available capital. All major exchanges these days are electronic, so you don't have to worry about which provide APIs, because it's highly unlikely that you'll working directly with them (at least until you're bankrolling some decent change). Interactive Brokers is the preferred brokerage for professional retail and small-midsized prop firms and hedge funds, specifically because they offer a decent API (cross-platform, which is rare since most non-fix providers target Windows) for free and FIX connectivity if you're doing more volume. IB gives you access to trade on virtually all large international markets with very competitive commissions. For about $10/month (fee waived if you have a few trades/month), they'll also provide an acceptable data feed. If you're wanting to focus on specific instrument types, such as only futures, there are alternatives.
There are various open source and cheap commercial platforms you can take a look at. The simple open source trading platforms are ActiveQuant (java) and TradeLink (c#). There is also MarketCetera (java), which is a professional platform, but most retailers don't find it very attractive, because they only provide a generic FIX adapter and a base market data feed adapter which needs to be extended for your specific needs (there is also no backtesting, proper data storage). There are a few commercial solutions targeted at retailers, such as NinjaTrader (free for sim-mode with free futures tick/historical data), OpenQuant, and AmiBroker. These aren't appropriate for complex high frequency strategies, but you'll get some good experience coding strategies immediately to gain some experience instead of having to tinker with the infrastructure.
All that being said, it's difficult to break into the high frequency and statarb space if you're just beginning. People always assume it's just a technology problem, but you'll soon enough find out it's not ;) So, I'd suggest that you take it a bit slower and work your way up from daily data trading to intraday to high frequency, a journey that will surely take some time and keep you challenged along the way.
I'm a CS guy by schooling and got started in the industry a few years ago. For me, trading is a very challenging, but extremely fun and rewarding. The markets are so dynamic that you'll constantly be going through the R&D cycle and you get to use all that CS/Math theory you learned, instead of hammering out generic run of the mill code like you do at a lot of jobs these days.