Battery recommend
 

Does anyone has suggestion what battery to take for this kit ??? Are connection usually the same , so it does fit (connects) even with newer battery ?

AW 26"x1.75" Rear Wheel Electric Bicycle LCD Display Motor Kit E-Bike Conversion 48V1000W

https://www.amazon.com/gp/product/B00Q8JT9H2/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

In general, the connectors won't match unless you buy both battery and kit from the same source (as in company, not Amazon or ebay). Doesn't matter to me since I've been purchasing batteries mainly from Luna Cycle and they use my preferred connector, XT-90 (with XT-60 for charging), so I just crimp the same connector on the controller.

I bought a 48V 20Ah Unit Pack Power triangle battery for my 500W Bafang geared rear hub conversion. No complaints, and I added a note when I bought it requesting the correct connector for my controller. They included an adapter, so no soldering. They don't use the best name brand cells however, so longevity is an unknown. They state that they use "powerful Chinese cells", which I found slightly comical. I get ~50 mile range if I pedal and keep speed below 20 mph except on downhills. YMMV

Good point about some manufacturers putting a preferred connector on their "output" port, and I did that with UPP once too (but forgot about it). Your battery (960 wh 20 X 48) providing 50 miles seems about right for 18 - 20 mph under "normal" conditions (relatively flat terrain, 180 pound rider, little wind etc) since the "experts" state those conditions for a hub motor should require about 20 wh per mile.