The trouble with cheap bikes is that they are often terrible. Edinburgh Bicycle Co-op's Courier is the exception that proves the rule.
Mountain bikes make good commuter bikes.
Or rather, they can do. Fat tyres are good for crashing through potholes, and frames built for surviving the rigours of off-road riding will happily cope with the occasional kerb. While individuals will always adapt bikes, there's some hassle and usually some expense in doing so. Wandering around the internet, we came across a street-style mountain bike that won't break the bank. We did a double take when we saw the price.