New to Fixies

[Cycleops]

As long as the wheels have been well made and are not having any loose spokes you should be fine.
Don't see how a XS which fits 5’1 rider would do for you at 5’3.

 

[12boy]

At least get a front brake if you are riding fixed and a rear brake would not hurt, at least until you get some fixed gear muscle memory. Sugino crank arms coupled with a 103mm BB can help you get to the correct chainline if your rear wheel is 120 mm wide. I used to ride fixed but it is hilly here and I don't love going downhill at 140 rpm. SS is more my taste now. Before you take off for work on a fixie, I would suggest you get accustomed to the fixie first.