your right about not getting to smaller a cc, but dont go over the top, you just admitted you aint got loads of cash, which bigger bikes can cost, and carry on costing to keep running, buying a cheap higher power bike is gonna cost when it goes wrong, also, dont just "expect to pass" we sold wasp's (my missus) bike, a 250cc hornet to a young lad who knew he would pass, he's now on his 3rd attempt
I'd look into a 600cc, but with the restrictor plates in, bringing it down to the 33bhp, it'll still do a ton (100mph)
Im gonna say, look at second hand HONDA HORNET 600, if you look around 98 2000