I am building a single speed 74 Schwinn Traveler for my son to use as a campus bike/single speed. I had a set of alloy 700 wheels with a 7 speed freewheel in the garage from another project that I am using on the frame and dumping the steel wheels. I already hung the wheel set and they will fit with a little tugging of the chainstays AND the brakes have enough adjustment to work and I am pretty sure that the dropouts will have enough adjustment to avoid using a tensioner. It appears by eyeballing things that I will have to use the smaller chainring (38 teeth I think) on the crank to line things up when I put the freewheel on. What would be the recommended size/brand of freewheel? The bike will only be used around campus (no hills) for probably no more than a couple of miles at a time with moderate loads at best. I know NOTHING about single speed/fixed gear stuff as all of my experience with bikes is OLD mountain/road bikes, monstercross, and touring rigs.

Also I am a bit confused about the single speed freewheels at this point. I see “BMX” freewheels offered for sale. Do these use the same freewheel body as a regular freewheel or is it just a marketing thing? Also, It seems that there are two or three different type of freewheel tools used among the manufacturers? Do any of them use the standard freewheel tool or I am going to have to buy another tool? (I can always use another tool, right?). One of the manufactures uses what appears to use a four prong tool that looks like maybe my old Suntour freewheel tour? Can I find a decent single speed freewheel for 15 or 20 bucks?
I’m sure that, as common as this bike is, that hundreds if these conversions have been done already so I apologize if I am being that guy that asks the same question for the millionth time.

Thanks in advance! Maybe??