My response will be boring but ...

Go to a local ghetto bike shop and talk with the staff, maybe they have old or used fixed gears parts, that's what I have done for my first fixie. The dude at the shop just had a couple of frame and I took one of the cheapest 45mm deep v rim flip flop hub for my wheelset ( the one used on purefix and zyclefix bike ). First fixie, I suggest flip flop. Nice to see that you have a frame and only needs the wheel/chain. The first adjustment can also be a pain on a old frame if you don't have the right tools, spacers ... It can cost you 40$ cash at a bike shop ...

But if you still want to build it yourself, on a budget under 300$ for everything and room to get a 40-50$ maintenance and good tires.

Pure Fix 700C 50mm Wheelset | Pure Fix Cycles
Fixie Crankset 44T | Pure Fix Cycles

For the chain you can order

KMC Z410H Chain | Pure Fix Cycles

But I would go to a bike shop to get one custom fit since you dont have a standart fixie frame.