I started off on CBT and 125ccs, have to say I doubt I could have passed DAS easily- I'd never driven either and it's a lot to take on. I assumed cycling experience would help but if anything it was a hindrance.
One thing, used 125s don't devalue much, so if you buy one and sell it after a year you're unlikely to lose out unless you buy badly, or destroy it. Personally if I was doing it again I'd get a DT125 or similiar, the downside is that they're commonly stolen as Onzadog says but they're pretty capable machines- light, good riding position for traffic, and they don't look like scale models. A good introduction to real bikes. The race rep 125s are pretty much all horrible, except for the RS125 but even then only when derestricted.
Or here's always the riding school classics, SR125s and the like. Not much fun but at least they look "right", they're indestructible and they're cheap.
I see people say "DAS + 500", I'm not sure that's good advice, most 500s on the market are basically stoneage. They can be good fun but as a rule, they're not. Someone usually says "they race cb500s" and it's true but then they also race Harleys and mopeds. Personally, I reckon if you're going to go DAS it makes more sense to look at an SV650 or a Honda Hornet, or a Fazer/Diversion- all much better bikes than the 500cc competition and not drastically more expensive (sometimes cheaper, you can get a surprisingly decent SV650 for under a grand these days, it'll look like it's been in the sea but it'll work)