There are bunches of tying thread brands out there, so talk with your fly shop and see what the tiers there like to use. I like Veevus thread because even in small sizes I can’t seem to break it very easily. Having the thread break, especially at the end of tying a bug, is truly demoralizing. Like your ice cream falling out of the cone. Avoid it.
I use 12/0[^1] thread for most all of my trout fly tying. I’ve used as small as 16/0 and as large as 10/0 and it all works just fine. The thinner the thread (higher number before the “/0”) the less bulk you’ll add. This is a good thing on smaller flies but not so good if you’re using the thread to build the shape of the body. It will still work, but it takes more thread wraps.
The #/0 measuring of thread can usually get you in the right size ballpark between brands, but the denier measurement system is more accurate [1]. The Veevus 12/0 thread I use most (of course) doesn’t have a published denier rating but tell the folks at the fly shop you’re tying flies between size 14 and 10 and they will help you put the right thread on your bobbin.
As I mentioned in What a Tool- Bobbin (Holder), having each color of thread already spooled up is, as they say in the old country, baller. I usually have a light, mid and dark color of thread ready to go. You can get away with less, far less. None of the flies in the effective fly box really show the thread color so you can get away with white or tan, probably even black as your only thread color.
[^1:] J Stockard has a great resource here: Fly Tying Thread Comparison Guide + Free Downloadable Chart
More references Understanding Fly Tying Thread with Charlie Craven