I want to create a character that wants to go to the moon, eventually start setting up some sort of settlement there, and ideally being able to live there in the end, with or without occasional trips back to "Earth".

The transport is pretty obvious - Teleport allows a near guaranteed success on places you can currently see, and I can see the moon, at night (I understand some Dungeon Masters might object to this - I know for a fact mine won't). I've figured out how to survive up there for at least just under three minutes - Resilient Sphere, a 4th level spell, includes the following:

Nothing, not physical Objects, energy, or other spell Effects, can pass through the barrier, in or out, though a creature in the Sphere can breathe there.

Assuming these two spells, a succesful teleport, and efficient turn management, a trip for maximum time (without assistance) would go like this:

Turn one: cast Resilient Sphere on self.
Turn two: cast Teleport, teleporting to the moon.
Turns three through nine: other activities.
Turn ten: cast Resilient Sphere on self again, during this last turn of the previous one being up.
Turns eleven through nineteen: other activities.
Turn twenty: cast Resilient Sphere on self again, during this last turn of the previous one being up.
Turn twenty-one through twenty-nine: other activities. Turn thirty: cast Teleport, back to "Earth".

This makes perfect use of a level 20 Wizard's three level four spell slots and two level seven spell slots. This is also, however, where my current 1 AM brain hits a wall. Any advice anyone might have on how I could further improve, in absolutely any way, is hugely appreciated. Thank you!

EDIT: /u/euphoric_pessimist mentioned the Necklace of Adaptation, an uncommon magic item which allows you to "breathe normally in any environment", a very good solve for the lack of oxygen.
/u/mrdeadsniper brought up Leomund's Tiny Hut, but it would be difficult to cast - you just barely run one turn short for the full casting of it, since you have to re-up your Resilient Sphere on every tenth turn to keep you alive. Three levels of Sorcerer would allow you to use extended spell on your initial Resilient Sphere to double the duration to two minutes, giving you enough time to cast Tiny Hut. A problem arises with not being a level 20 wizard for the third level 7 slot, but this is solved by also using extended spell on the casting of Tiny Hut - this lengthens it to 16 hours, giving you more than enough time for a long rest to get your single 7th level slot back for the return trip.
Some questions remain - How would you go about stopping the pressure of the vacuum of space from annihilating your fragile d6 hit die body when you want to walk the dog? Are there ways of requiring even less high of a level to do this? Should I be going to sleep? I'll be honest - I only know the answer to one of these questions. Goodnight for now, any help is still welcome!