Projects like this can take a number of directions depending upon how much work you want to put into it. If you want to, you can use the existing rear wheel but if you want to go with the option of switching from fixed to freewheel, then you will want a flip-flop hub.
I ride a Miyata conversion. It is absolutely wonderful. I have zero issues with chainline, chain taughtness or anything. It is full-time fixed, no freewheel at all. When I want to ride SS with a freewheel I have two other bikes for that. If the wife said I had to narrow down my herd to two bikes, the Miyata would be one of them. If she said one it might be a close call.
Go visit Sheldon Brown's site. He gives advice on converting a geared bike to fixed. He also has a handy gear calculator. Check out his "gain ratio" calculator too where he takes into account other variables.
https://sheldonbrown.com/fixed-conversion.html
Good luck.