I usually default to a 28 or 32 TPI thread size for an internal part like your assembly, which tends to be okay as long as you can get 0.150-0.200 length of threaded section. For stability it's good the have more threads available, but you loose actual threaded length when you add in any relief grooves at the start or end of the threaded area. But having a full 0.150 section threaded with a 32-TPI thread will give you a good 5 rotations which might be enough. Good place to start anyway.
You can see if something like that will fit by taking your male threaded component and sizing its diameter to the nominal major diameter (1/2" dia, 7/16" dia, etc) and assume the threads would be [1/TPI] deep on the radius. In reality the threads won't be that deep so it leaves some wiggle room.
The male side is easy because the diameter is nominal, minus a small allowance if you really care. But the female size you'd have to look up in machinist handbook (or calculate if you're into that sort of thing). I prefer to look it up in a spreadsheet that has the allowance fits. Lemme see if I can attach it to this post
Acme can be tricky because there's supposed to be a proportional link between the thread depth and thread pitch, specifically pitch is supposed to be 2x the depth (before all the allowances and other details). It'd definitely give you a lot of strength but it might not be necessary. Some shops hate dealing with parts liek that since you have to get creative to measure the thread, if it's out of their comfort zone...