One of the most common bicycle electric conversions is a direct drive brushless hub motor such as the ones in the wheels pictured. They offer quiet operation and great power but weigh more than geared systems.
Hub motors also come in geared drive versions that are lighter weight, a bit slower than direct drive, but more efficient. This means your battery charge will go farther. These have a quiet whine noise from the gearing.
The cheapest, heaviest and least environmentally sound alternative is sealed lead acid (SLA) - as reliable as you use in a car.
Currently, LiFePO4 battery chemistry (Lithium Ferrous Phosphate) offers a good amount of stored energy per pound, and is both safe and environmentally gentle. These battery packs incorporate a battery management system to function consistently at peak potential. Because of the intensity of e-bike requirements, LiFePO4 batteries are generally guaranteed for about 1500 cycles and maintain 80% capacity to 2000 cycles or beyond. That said, SLA batteries are good for 200-300 cycles and cost about $200.00 for a basic, but complete, 36 volt system. LiFePO4 costs about $500 for a top end, 15 amp hour, 36 volt system that includes charger, wiring and warranty.
AllCell Technologies offer improved, safe, lithium ion batteries. Protected by a proprietary thermal management technology, AllCell batteries provide the best combination of energy density and cycle life in the industry. They can pack more energy into these cells so they are lighter yet, but more expensive.
Simple math: LiFePO4 batteries are good for about 5 times the life of SLAs. That translates to $1000.00 for SLA batteries vs. $500.00 for a much more environmentally friendly and approximately one half lighter weight installation. Weighing even less, AllCell lithium ion batteries are about $700 for a 15 ah, 36 volt system.