****, I usually just lurk in SS/FG but frankly:

Conversions are fine. But since you have zero idea about chain tension, chain line, what it'll take to dish and fit a rear wheel appropriately to convert anything - that's out of the way for you unless you can find someone willing to impart the knowledge of do the conversion for you.

Cheap is cheap. There is no 'cheap and good' imho. I have a 'cheap' Origin8 fixed-gear commuter bike that was designed by them to be just that - and it sucks still mostly.

I have a Surly Karate Monkey that I invested a LOT of money in and it's worth every penny or more to me.

I also have a LHT and can see the value of having a quality geared bike compared to a 20 year old beater geared bike.

With that said, I'm going to go out on a limb and say, even if you worked for a LBS like I do, that $200 isn't going to stretch.

Save up and buy a C'mute Pake frame and fork. Look around, use the search function and find out what BB/Crank/Hubs/wheel set.

That's the 'cheap' way to go, and without sitting down and doing the math for you - I'm going to wager that you're still looking at a $900ish investment to have something that's not a total piece of crap and will put up with commuter mileage.

Of course, I'm nobody honestly - someone else can probably give you a lot more information and tell you that your $200 investment is WAY more than is needed for a B/A whip.