Should be in the SS/FX forum

But I would go Single Speed and turn it into a specialized SS. Like with low gearing for hill climbs

If you want to go SS, a hub that's fit to be a Shimano Freewheel, the SS freewheel should spin right on.
If you want to go Fixie, then the hub is either sacrificed to make a suicide fixie or get a new hub.

I say this:
If you want a bike just because. You don't need it for anything and just want it. Go fixie
But fixie is quite expensive
For a fixie, you need:
1/8 chain
rear hub replacement
re lacing rear hub
or
new wheel set
then:
pedals with clips and straps or clipless
and brakes, you need brakes for a fixie
gear ring and set up for gear ring

a single speed you just need:
freewheel
1/8 chain
and shorter tappered bolts for crank. I paid $8 for them, and it's best to have. Otherwise you need to cut the old ones.