Sprockets are either 1/8th or 3/32nd.
You can use a 3/32nd sprocket with either a 1/8th or 3/32nd chain.
A couple of learning points .....
You may not have experienced a "tight/slack" chain yet. But chainwheels are never perfectly round and there will be tight spots at some point. When tensioning the chain, locate the tight spot and pull the wheel back as hard as you can and tighten. If you happen to tension the chain when at a slack point, when the pedals are rotated, you'll experience a "grating" noise at the tight spot.
With the lock ring, essential with only one brake, only tighten with "fingers". Don't use any force applied with tools. When back pedaling, the sprocket will hit the lock ring and apply force in the direction that tightens the lock ring naturally.
My experience .....
I started off on fixed, back in 1960, so have always had a fasination for fixed. When I first got gears, couldn't work them out. Didnt know when to change up or down, but eventually became confident with gears and my early years of time trials were all on gears.
Many years later (90's), still timetrialling, I rebuilt my Mercian track frame for fixed and kept it for a dedicated time trial bike. Much cheaper and simpler having a fixed bike rather than a geared bike. I also found out that on a flattish time trial course, that fixed was no slower than a geared bike and on a perfect "float" day, being much lighter was quicker.
Many many years later (00's), bought a Giant Bowery 72 on the cycle to work scheme. Rode it fixed for a season or so, but the Kentish Hills are just too severe to make fixed riding enjoyable, so switched to a single freewheel. This is now my GoTo bike for up to one hour rides.
Still have a dedicated fixed time trial bike, which unfortunatly hasn't been ridden in anger for a couple of years. This is set up with a single brake, tri spoke, deep section wheels and a modest 88" or 95" gear!
Enjoy