DC motor with battery
Have a look at e-bike specs. The main differences between inexpensive ones and costlier ones are the motor output and the Wh rating for the battery. Inexpensive ones will have motors as small as 250W and batteries rated for 250Wh; higher end ones will have motors up to 750W (more about this below) and batteries 500Wh or more.
Be aware also of the statutory limits on power for e-bikes. Many, if not most locales set a limit of 750W (about 1 HP) and have restrictions on top speed vs. assist.
More here: https://www.wired.com/story/guide-to-ebike-classes/
There are many e-bikes on offer that can exceed that, but get around the law with a ‘legal’ software-limited mode that you’re supposed to use if you’re operating on public streets and pathways (and you pinky-swear to set that mode.)
While you could home-build something that exceeds the e-bike limits (and there’s a whole culture devoted to doing exactly that), you’ll be building something that should be classed as a motorcycle and thus requires a license and insurance.
As far as the details of battery pack voltage, that depends on the motor + controller combo you settle on. Higher power setups will tend to use higher voltage packs, as it’s easier to increase voltage than increase current. Once you settle on voltage, then you’d choose the battery Ah or Wh rating that suits your range needs vs. desire for light weight.
You mention the specific case of 1kW motors that are rated for 36V or an alternate that’s rated for 48V. These will have different current requirements, so you’d need to choose a pack that can supply adequate current without overheating. If all other things are equal, choose the 48V option as it uses lower current.
Finally, you have a choice of front hub drive, rear hub drive, mid-drive or tire (friction roller) drive.
Front hub drive is probably the easiest as a retrofit as it leaves your chain/ sprocket/ derailleur intact, but it adds unsprung weight and affects handling somewhat.
Rear hub drive requires you to re-engineer the pedal drive stuff, doable for a single speed or hub shifter but not so much a derailleur setup. Again, it has added unsprung weight and affects handling, though less than a front hub. It’s popular.
Mid drive is preferred by many because it has the least influence on handling, but it stresses the drive chain and sprockets and thus increases wear. It also may require a different frame to accommodate the motor + crank setup.
Tire (friction) drive is simple, but isn’t capable of higher power and gets dirty. They don’t last very long.
BONUS: a comparison of e-bike retrofit kits and types. https://www.thedrive.com/reviews/38415/best-ebike-conversion-kit