I wrote further up the thread that for what you say you want I would fit a crank drive kit. I’m not sure how much they cost with the battery but you could get a good one from Woosh with a full warranty for under your budget. So a s/h eBay bike and a bit of fettling if you don’t have one and you’re alway. Woosh has a new slightly cheaper CD motor kit which is selling well and has good reviews. It should be well powerful enough for you to keep to around 24mph on the flat with the right gearing if you derestrict it and are happy to be illegal. It will eat battery power at those speeds so you’ll need a big battery.
Search for CD kits, and threads on converting them. There is one not far up the forum where someone converted a Cube using a bb 01 CD kit. They are not hard to convert.