As this is the very first time I've ever started Skyrim from the very beginning with SkyUI (not to mention MO!) installed, along with mods that you can switch on and off via the menu during the game, when is the best time to do all the adjusting of the SkyUI mods at the beginning of the game? Is it during the ride on the cart, before I choose my character's identity, or after my escape from Helgen? I ask because some of these mods are actually game changing and I want to activate them in time so they don't muck the game up.

I always do it when entering the keep and hands are freed, As that is the point the game starts functioning normally and all mods have had time to initialize.

Or when using alternate start as i usually do, right after all the initialization messages have been printed, before doing anything else.

Yes, that is also point when you can save the game properly and exit and then reload and continue; and there is no more Character Generation or running from Alduin to do at that point. In fact, some mods do not kick in until you save and reload. At that point, you choose a side by choosing who to go with. And once inside the keep, you have a breathing space where you can fiddle with mods to your heart's content.

Many people say that if any mod causes problems when escaping from Helgen, Out It Goes! You also have a saved game where there are no mods in effect. Except maybe the Unofficial Patches mods.

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Okay, I'll remember that, change them once I enter the keep. Speaking of alternate starts, I have a secondary character all planned, one who wont be Dragonborn but will still live in the same reality as my main Dragonborn character. For him I'll be using Skyrim Unbound because, as far as I can remember, that offered the best choices for what I was wanting. Seems like that could prove a bit of a problem when it comes to deciding when to mess with mods. So, anyone got any advice when it comes to Skyrim Unbound?

with skyrim unbound after you have spawned in skyrim.
with LAL after character creation and before going to bed.