It's the same story as with everything else: you get what you pay for. Sometimes you can get lucky and find something used for cheaper that suits your needs well, but it doesn't happen like that if you don't really know what you're looking for. Most people I know who can't picture spending a few hundred bucks on a bike because they've always gotten dirt cheap hand-me-downs always have bikes that don't fit or don't work well or aren't well suited to their needs, and they're always wondering why biking is harder for them than it seems to be for other people. Or else they're always spending more money to try and band-aid the problem.

But when you think about it, $400 is actually amazingly cheap for a reasonably decent, reasonably light, new bicycle. You get more for your money in terms of quality and light weight in fixed gear bikes than in equivalently priced hybrids or cruisers or whatever, because the fixed gear has so many fewer parts and they're less sensitive to fine adjustment (i.e, no shifters, shift cables, derailleurs, only one cog, etc). So unless you honestly can't afford it, just spend the money and buy something that's decent to start with.

A road frame converted to fixed can be a really nice bike, but it's generally only really cheaper to do that if you're the sort of person with bins of spare parts kicking around your house. But it can be a good way to get more options if you want specific things.

And yeah, use brakes. It doesn't mean you can't still get good at stopping with your feet if that's your bag. You don't have to use them when you don't feel like it. But ultimately, no matter how good you get at skidding, you will always have more stopping power in front than in back, and more stopping power (not to mention control) with a wheel that is rolling rather than skidding. That's just physics.