Last week I bought myself an adenium. (replacement to one that died. :-( The leaves had a few spots on, but overall seemed healthy. Sorry about the large photo's - don't know how to shrink them.

Then this happened - leaf fell off. Drastic measures required urgently (from my last sad experience)

I've unpotted and washed - there is some rot at the bottom.

Where and how do I cut it off? Do I take the roots as well? When I repot - what size pot should I get? The plant is about 30cm high (about 12 inches - I think)