I ride my fixed with Shimano PD-M324 pedals (I don't really need the flats, I just had them laying around). You definitely want the SH-51 lateral release cleats, not the SH-56 multidirectional release cleats. You can visually tell the difference. The 56s have a ramp on the underside of the front of the cleat, the 51s do not.
Until these start to wear out from too much walking (I pretty much live in bike shoes during the summer, put on about 200 miles a week, and wear at least one set of cleats out every summer), they work fine. As they start to wear, you will get inappropriate releases from the toe. Just replace your cleats when this happens. Not really a big deal.
I've had a fixed around since the '80s, and was strapped until about 2010 or so. I much prefer the cleats (after I got used to the change-up). They are far less fiddly, and don't require any attention when I am playing in traffic.
Edit to add: I think it is really wise to run at least a front brake (I do). If the chain breaks, or I pop out of the pedals and end up going run-away (granted it doesn't happen often, but it can), at least I have a better option than laying the bike down in traffic, or running into a stationary object.
Last edited by jwarner; 11-16-14 at 02:15 AM.