I did CBT and DAS a few years ago on a CB500.
If you do the test on an unrestricted 500 then there are no silly restrictions on what you can ride afterwards. Then just for fun or an urban commute, a 250 would be OK. Longer distances or trunk roads, start with a 500.
I started with Kawasaki ER5, currently on an ER6n which is a 650. It's not hugely heavy and fast enough for me
P.S. Sold the ER5 as a 1 owner 9 year old bike with a years MOT for under £500 on Fleabay so you should be able to pick something similar up easily.