Look, this isnt rocket science; when TTW is correctly installed and sans mods that mess with the FNV starting sequence, you start in vault 101.
AtaKitH also completes fine sans mods that mess with the FNV starting sequence.
I run a pretty heavily modded setup. At last count I had 107 plugins, and my only major problems (things like quests that cant be completed, reproducible crashes and critical npc conflicts rather than scenery gaps and similar) stem from hardware restrictions due to my aging laptop.
TTW is still in alpha. This means there will be issues even when it is the only thing installed. Having said that, the vast majority of mods will work A-OK with it.
There are some FNV mods that repurpose unused FO3 records still present in the FNV esm that can cause major issues with TTW, and there are some (you personally seem to use at least one) that edit either the CharGen quest or mess with one of the new-game-scripts (thats just what I call them). These need to be changed on their end or they will not work correctly (99% of the time).
Keep in mind that I am not a member of the Dev team. I am sure one of them will end up posting here and they can get into all the nitty-gritty technical details for you, but basically: TTW works pretty darn well out of the box and the stuff it doesn't work well with usually need tailored compatibility patches, which should be made (and have been), but aren't really part of TTW proper.