i’ve been running a 1 x 9 set up on my commuter/hack bike for the past 2 years. I’ve ridden over 7,000 miles and really like the set up.
Firstly I would buy a decent rear mech and shifter off the classifieds, miles cheaper.
I’ve got a 42t front ring, go for a downhill/slalom style one as they are a bit wider. I have a blackspire one and its been ace. Obviously you’ll need some shorter chainring bolts to go with it. 42t seems fine for what I do but you’ll probably need to experiment before you find what works best for you.
Depending on what sortb of riding you do you will need a chainguide of some sort or other. As most of my riding on this bike is fairly gentle I just used an old front mech tensioned up to the cable stop on the seat tube which works well. I also drilled out the cable stops to the rear mech to give a continuous cable run and fitted some cable oilers – minimum maintenance is good!
Or perhaps an alfine?