I could really use a house about now in my game. Can anyone please let me know what quest(s) or whatever I need to do to get a house or at least a place to put my excess stuff?

Any container/house can be used because they don't reset anymore and eat your stuff. As for dedicated player "houses" Mr.House gives you the lucky 38 VIP suite, you can get one at the other casinos, and most factions have a faction Hideout. Also you can get a permanent room in Novac.

Would that be the hotel room you need a key for?

Alternatively, if Ringo has cleared out of the gas station next to the doctor's house in Goodsprings, there's a mattress and a safe that doesn't respawn.

The Hotel Room in Novac.

You also get a penthouse suite at Lucky 38 upon entering New Vegas.

There might be more, but that's as far as I've seen.

Victor's Shack in Good Springs.

Go to the atomic wrangler and do one of the missions for the garret twins. They will give you an apartment if you finish the mission.

MechaCannibal...completely off topic but dduuudddde.....your avatar ROCKS!!!!! and I am still looking for a upgradable house. The Hotel Room in Novac is working in the meantime.