I'm running 74 mods and am stable.
The biggest issue you'll have is in mods that change the same element. There you have 2 options, a compatibility patch or a mod manager mod.
Compatibility patches can usually be found in teh Optional files section of the mods Nexus page, for example, the Weapon Mod Expansion mod has patches for FOOK, EVE, Named and sorted.
Mod management mods are a little trickier, usually the mod page will list which one you need, but sometimes you will have to trawl through the comments to find instructions on how to interface a mod to the right management mod. An easy example is "The Mod Configuration Menu" which works well out of the box and resolves multiple mods wanting to use the in game menu.
A hard example is the UIO User Interface Organizer, which is less supported and often requires you to do the interfacing yourself. (It resolves multiple mods wanting to tweak the UI)
You'll be fine so long as you only have one mod per thing, 1 UI mod, 1 pipboy mod, 1 weather mod ect, OR if they provide a compatibility patch. Sometimes it will be fine anyway, one mod will just overwrite the other one out of existence, other times such overwriting will have unexpected results.
Best tips are to: