For the battery one idea could be 12V DeWalt after market replacement batteries. I recently bought two for my decade old drill for $25 or so online. There are wired sockets available too that allow you to snap them into a holder. Three of those might carry a 36V 250W ebike a fair distance on flat ground. Lithium is a better battery but aftermarket 12V NiCD might be easier.
I have two ebikes.
The first is a Jueshai 48V 500W rear hub drive with a "silverfish" battery that locks to the frame right behind the seat post. Unknown brand cells in the battery (Sanyo?) but they are 18650. It is the same bike that the delivery people use in NYC. It is approaching 2000 miles. No troubles aside from minor bicycle wear and tear i.e. tires/tubes/rear derailleur. We've upgraded a few little things - seat, handlebars, tires, added fenders, rear rack. ~$1200. I'd buy it again.
The second is a Bafang BBSHD 1500W middrive with a dolphin style 48V14AH battery on the downtube. 18650 Samsung cells. Bought the kit, installed it on my old mtn bike. Steep learning curve about bicycle components during that project.
Added commuter accessories and touring tires when the old knobbies wore out (quickly). I have over 3300K miles on it. ~$1200 invested. I don't intend to replace it at any point. I do wish the frame was just a smidge larger. I see lots of ready to ride ebikes that are very appealing to me but the pricetag is dizzyng and I don't like the proprietary nature of their batteries or components.
If I was building an ebike that would be at risk of being stolen, I'd focus on a $50 ten speed, 250W drive, and some sort 12Vx3 DeWalt battery - or tiny Milwaukee "Fuel" (lithium) batteries that I could pocket each time I parked. Consider a friction roller type drive that is self-contained and easy to attach and remove.
My bike always comes inside with me at work, the other bike is locked up at our teen's school. No problems so far.
FWIW there is a long list of forums to read:
Endless Sphere is a great one.
https://duckduckgo.com/?q=electric+bike+forum