Re: $1,000 motorized bikes
For a grand, I would go with either great bike and so-so gas motor or vice-versa.
Electra Ratfink with a two stroke in the frame and drum brakes would work.
Conversely, I could use a Sun beach cruiser with a Honda thumper in the frame and shift kit. If I settle for a chinese thumper, I might be able to swing the drum brakes.
I don't think I could do a very fun ebike for a grand. Lithium batteries quickly devour the budget.
“You're only young once, but you can be immature as long as you like" -Unknown