Load in this order: CBA, TFAR, ACE, RHS, CUP Terrains, maps, client-side mods. (if this doesn't do it swap TFAR and ACE. I can't remember the more reliable method but I think they're interchangeable).
Typically though being stuck on the loading screen is more about network problems than mod problems. Mod problems usually just boot you out.
Penny is correct. If your mods aren't lining up with the server, you'll get booted before you get to the slot/affiliation selection screen. If you're getting stuck at a black screen after selecting your slot and clicking join (or whatever the text says) then you are having other issues. Validate game integrity, try loading into a self-hosted server and see if results are the same.
The Recruiting server uses a different mod set than the standard 15th for the Official Task Force servers. So this means you may have 2 versions of CBA or ACE in your available mods, and you need to load the correct version for Standard 15th vs. 15th Recruiting Server. Confirm that your Recruiting server set is the same as listed below, then try loading in again.
Check this thread for the list and links: