Begonias are easy IF you get the right variety for your conditions. There are a lot of cane begonias, and it's not possible to say 'this is the right size pot for a cane begonia', but generally you probably shouldn't pot it in a pot more than a couple inches bigger than the root ball. With some canes--the ones that can get very large--you can 'throw caution to the wind' so to speak and put them in quite large pots if your potting mix is very quick-draining. I was told when I was starting out 'if you want a big begonia put it in a big pot'. That is not necessarily a good idea, but it works for the larger-growing ones. I have just stuck an un-rooted cutting of Lucerna, for instance, in a ten or twelve inch pot and had it make a big beautiful plant in months. I don't usually do that and don't really recommend it, but it'll work with some. I have some large-growing rhizos I can do that with too--but I certainly wouldn't do it with most. Your 'Jewel' rhizome--I forget which you said but there are several--Brown Jewel, Green Jewel, again I forget--are not large growers. They prefer plenty of humidity. Oh, and about pot sizes--I prefer to keep all my begonias in azalea pots or bulb pans or terra cotta bowls, basically shallow pots as that's the way they grow in nature with shallow roots running around in the leaf mold and detritus. Some folks prefer to grow canes in standard pots to balance their height, and if that works better for you go for it.