what 18650 brand cells are best for this application 36v 500watt needs to be 10s6p

I am running a 500watt brushed motor with 36 volt controller in a very old but great Schwinn e350 scooter. it goes fast but my cheap alibaba battery pack is dying after 3 years. i used to go very far but now i go only about 8 miles. I did not know about maintaining lithium packs so i ran my pack and kept bike outside in very cold weather. I am going to build my own pack for the first time. I also think i am going to get a charger that limits charge to 80% if that helps maintain the pack life and only charge to full if going to use it right away so it does not sit around full for long periods.

The scooter only has space for 10s6p set up. I want good range but also do not want to hurt the pack it I go up hill so i want it to have enough amps and good rate of discharge to handle use. not that I live in a hilly area but just want it to work well . Are these opposing wishes? it seems people say if I get higher amp batteries then they get hot. I am limited in space of the battery compartment which was made for lead acid batteries, so I cannot go more than 6p because the limiting dimensions are 4.5 inch wide and the other one is 2.75 inch height and 12 inch long. The alibaba pack did not fit in the compartment but in the back basket but i want to move the battery I build into the original battery compartment.

of course I want to go cheap but I can go higher in cost if that makes a difference.

Any thoughts on brands and where to buy. I see Liion wholesale. I live in Colorado in US. so wondering what is best way to buy 60 cells and all the needed nickle metal strips here.

I will build my own welder from a battery and solenoid. I have a lot of electronic and mechanical experience and have been watching youtube i think the build will be easy enough but the where to buy and what cells to get is what is the hardest for me to figure out.

any help appreciated!!!!!

36V from 500W is only 14A from the entire pack. Since you plan on a medium-sized 10S/6P pack, this is only 2.3A per cell. You have many options.

Only charge to 4.1V per cell, 10S X 4.1 = 41.0V

If you want max range, the current leaders are LG MJ1, Samsung 35E, and Panasonic GA (roughly 3400-mAh each). I would recommend the MJ1, but the oither two are also good.

Some of the lower capacity cells are more affordable per amp-hour (since current will not be an issue in this application). There are many low amp cells around 2200-Ah each. If you want to attempt harvesting used cells, go for the medical packs, they have consistently been the best quality.

https://www.youtube.com/watch?v=3oiioZds5Co&t=323s