what i found out was that there are 2 "standards" the airline industry uses to determine what goes with you and what doesnt. I chose the smaller of the 2 since i felt that i woudnt have an issue carry with me onboard. On my return flight, i dont care, but when im heading there, id rather not loose my check in luggage.
i didnt do alot of digging, but the smaller measurements i went by were: 22 x 14 x 9 inches.
Since youre gong to be gone for 2 months, i would try to maximize that size or even go with the 2nd and larger "standard" since due to your length of stay. I say that since youre on a "tight budget" you wont be able to stop and buy whatever you need and will have to bring it with you.
just an for your info, i have a pack/bag that fits the smaller dimensions and i use it on my 1 month trips with no problems. I do send stuff back home to eliminate carrying extra stuff at each stop, but this will probably be a luxury for you.
one last comment. I say... "buy once, cry once". with that said, if youre going to make a habit of doing more traveling, i would seriously think about getting a decent bag/pack -once.
the last comment/hint i can think of is to do a "dry run" with your packing and all of the stuff you THINK you will want to bring. You can use those reusable grocery bags (cloths/woven plastic) and fill/pack them and see how you will do with that pack. you can then measure the volume of the bag and compare it to the pack.