Couple of options:
I would look on craigslist if you're going to be in a relatively well-populated area (eg I live in the country, 1.5 hrs from where almost everything on our craigslist is listed, so it's hard). I would look on a Thursday or Friday and rent a car or pickup truck just for the weekend to pick up everything you buy on craigslist, assuming you can get 80% of what you need furniture wise from craigslist that one day.
If you can't make that work (either there isn't enough available all at once that's decent, or whatever) - will you be near an IKEA? I'd probably go to IKEA and get a cheap set of pots n pans (our "cheap" IKEA set is still going 12 years later) and inexpensive furniture. Put the 2.5 yo in the ball pit.

oh you'll still probably need to rent a car if you can't borrow one.