I have seen some very helpful videos on UTube by NewEnglandGardener about rooting cuttings and transplanting figs, have you seen them yet? Watching these videos may help you.
Terry

Just don't use very large pots start with reasonable size and after some growth you can re pot. Unreasonable large pots tend to accumulate water and get the roots to rot.

Best after up-potting, move plants to humidity box for at least 2 to 3 weeks. Make sure fast draining medium(perlite & bark mulch) used in potting soil & use 1 gal size pots. Good to use a ratio top soil 50% to fast draining media.Treehugger2012 advise is excellent. Larger pots hold much more moisture to kill young plants. Not forgetting make extra drain holes in plastic 1 gal pots. Perched water is enemy No.1. Filtered sunlight, especially morning sun is great.