Do you guys think it would be reasonable to budget for an initially purchase of around 25k, and then finance the rest of the necessary repairs?
Depends what you mean by "finance". If you take on any loans those are going to lock you to land while you pay them off. That's not to say it's a bad thing, but it needs to be factored into your plan. For me, I had 20k in cash and did a 10k loan. Picked up a good 32ft boat for 20k, put 6k in it right away and then used the other 4k to find a new job and move there.
But my plan wasn't an immediate "buy and go". I wanted to spend a year on the boat, work 9-5, and pay off a couple things and put money into the boat.
With 25k you could pick up something for 20k, get it home with the 5k for "gotta be done now" work and then you'll probably want to put more money into it before leaving. Maybe solar, maybe heating, what you want/need will be very custom to you and your girlfriend and your goals.
Or with 25k, you could pick up a smaller boat in the 10-15k range and put more money in up front and then just go.
But I think before all that you really need to get a better idea of your cruising grounds and the lifestyle you want to live. For me it's Bahamas cruising and living at anchor and (hopefully) working online. So my boat is a really good boat for that and I'm gearing her up for living at anchor. If my goals change down the road(maybe world cruising), I'd likely get another boat that supports those goals better and I'll work out a plan to do that.
So, where do you want to cruise? What kind of draft do you need for those waters? Any mast height issues? How much space do you need? Will you be living at a dock with shore power and water? Spending any time in cold climates? What are your lifestyle "needs"(I like good home cooked food, internet and watching some pre-recorded tv now and then).