For now, you don't have to swap either derailleur, especially since you're on a budget. You'll need to move the FD down a bit, and double check that the chainring spacing (separation) is the same or close on both the new and old cranks, and you'll use the two outer positions on the lever, leaving a phantom granny position, which you'll lock out via the limit screw. It's possible you'll have to use a longer inner limit screw to meet this objective.
You can always use a longer cage RD where a short one works, the only penalties being a very marginal loss of performance, some extra weight (including more chain that you'd otherwise need) and lower ground clearance, none of which matter a great deal. If you have extra cash to blow, an FD better matched to the new crank might be nice, but only if you find one really cheap.
__________________
FB
Chain-L site
An ounce of diagnosis is worth a pound of cure.
Just because I'm tired of arguing, doesn't mean you're right.
“One accurate measurement is worth a thousand expert opinions” - Adm Grace Murray Hopper - USN
WARNING, I'm from New York. Thin skinned people should maintain safe distance.