It's a cheap frame, better to make it a cheap bike. Buy a decent, but not expensive rear wheel. One that will last long enough for you to reuse. If the frame has a one piece crank, keep it as is. If it's 3 piece, just ditch the outer chainring. Buy a 3/8th cog, and reuse the chain. You can do a cheap conversion for the cost of a wheel, plus some chainring bolts.
Then, start saving up for a really nice fixed gear