That price will be very difficult to meet. For that money it'll probably have to be an AliExpress special. Get a front hub. You probably want a torque arm but I don't think you'll find any in that price range. You can get away without one if you run the motor at low power, like 250W. Unfortunately I don't think you can get a non-hazardous battery anywhere close to that price range. Perhaps look for LiFePO4 (LFP) battery since the chemistry is inherently safer and it's cheaper to make. It's heavier than standard Li-ion.

Otherwise I'd get:

• Bafang G311
• Compatible Bafang controller with torque assist capability. The lowest wattage will do
• Bafang display
• Bafang torque sensing bottom bracket
• Good quality but smaller battery. E.g. 300-400Whr.

With all that said, steep gradients can kill geared hubs so a direct-drive hub or a mid drive like BBS02/HD might be better suited. Most DD hubs are more powerful so you'd either have to use torque arm/a or run it at low wattage. In general aluminum frames can't handle a lot of torque at their dropouts without spreading or cracking. The rear dropouts can handle 500-700W when the nuts are correctly torqued. You can read about that on ebikes.ca.

IDK about that budget unless you're excluding the battery cost. You really, really don't want to cheap out on the battery. Save up your money and get a kit with batteries that won't burn your building down.

That said, a Bafang or Photon mid drive kit would help crush hills pretty well. Just keep in mind, you'll want to stay in compliance with your local country's ebike regulations or risk getting your bike confiscated, but even a quality 250w-350w motor on a mid drive can make a big difference because it can take advantage of your bike's gears, unlike a hub motor.

Hmm, i think 200€ is quite hard. I did my old BMX and it did goes under 200€(overall around myr950), but it's a front hub, 250w 36v motor, 20inch wheel, and using sealed lead acid battery. I did everything myself, including building the wheel. The spoke i have to use custom size but i trim mine down from what's available on the market, tension it just right but it's not adjustable. To get the same setup but with lithium ion battery it might cost around 250€ - 300€, depend on the capacity and battery market around you.