Thousand quid is on the limit, I'd say. Amateur resto too; mudguards aren't right, seats are poorly covered and the battery is for a Honda 50.
Trouble with tiddlers is that you soon get fed up with the lack of performance, though if I wanted a small stroker I think I'd chose the good old Bantam.
Loads of new and used parts available, the range is big enough to encompass a lot of personal choices, and you could find one for less than £1000.
Your choice though.