Did it never cross your mind to think that maybe Rey built the speeder or that she got it as a gift or in a game of chance?
Also the film never tries to suggest that Rey is emaciated? She’s slim, yes but the point of her introduction is that food is hard to come by; not that she’s starving to death…I’ll give this 5 more minutes.
EDIT:
Rey getting BB-8 to the Resistance Base is a short term objective. Easily doable within days if not sooner. Her working with Han as a First Mate would be a prolonged endeavor…there is no problem with her motivation in that regard.