Everyone will have a different opinion but I'd have to help you narrow it down to Kauai or the big island for you. I don't want to say one or the other exactly so do some study on each and see what's best for you.
Maui I have often termed as "honeymoon central" and the way I stayed and what I did was not cheap but could easily be done cheaper then how I stay. So I would not look at Maui first, unless you want it to me a honeymoon
. Oahu you say you'll be on it for a while. So to me it's between Kauai and the big island.
Personally, I'd have to say that Kauai is more of my preference but you could probably do the big island cheaper (and I spend more time on the big island then Kauai so that might have something to do with my opinion as I don't get to Kauai as often as I want). I'll qualify that by saying, I spend more $$ on Kauai then I do on the big island. If you do your homemwork I'm sure you could find Kauai on a budget to be more then acceptable. But each island is different so you gotta figure out which one suits you folks then ask about that island.