A battery is to your e-cycle as a beating heart is to your body. You don't want a bad one or one likely to go bad even though there can be life after battery failure. Cheap e-bikes come with cheap lead acid bricks that might last a year and weigh four times more than lithium. Current batt tech favors lithium chemistries, and there are cheap ones. If you are feeling lucky, you can get three cheap ones from AliExpress for the price of one good one. The three will have no meaningful warranty, and the three together may or may not last as long as the premium one that is lighter, more efficient, better engineered, reliable, and has a two year warranty, so it almost certainly will last longer. Often going cheap will cost more overall and seriously disappoint you, so go premium if you can. But by going cheap you'll end up with more doorstops, so good luck with cheap if that's what you gotta do.
Heat reduces lithium-ion battery life, and the higher the charge, the worse the effect of heat (above refrigerator temperature). So to minimize battery longevity, use it on an e-bike, keep it outdoors when the temperature is above room temperature (room temp is not dramatically bad, but being in sun on a hot day is), and keep it fully charged whether it's being used or not. It is best not to fully charge a battery, however, but to store only what is expected to be needed the next day/next use. For maximum longevity in storage, charge to 50% SOC (state of charge) rated capacity, so always recharge to 50% SOC after use, then add more if and when needed.
Think of a bell curve with full charge on one end and full discharge on the other. Best to avoid both. The middle of the bell curve is the hump, so 50% plus or minus 10% is excellent, 50% plus or minus 20% is good, and 50% plus or minus 30% (20% to 80%) is not so bad, but plus or minus 40% is pushing bad, and plus or minus 50% (full charge and discharge) is maximally bad. So for 'not so bad', charge to 80% capacity, and discharge to 20% of really dead (nominal 0 SOC) or to when the BMS (battery management system) cuts off power assuming the BMS is one that protects from over discharge. There is good evidence that charging to 80% SOC (or even less) makes for a happy battery, but the belief that you should discharge to no more than 20% rated capacity is not actually evidence-based. So if your battery is rated for 54.6V full charge, and about 40V discharged, the BMS is allowing maximum charging but disallowing serious discharging to 33V - 35V, so discharging to 40V is not abusive. Charging to 80%, 52.0V, would not be so bad as going to 54.6V when the range is not needed. Being kind to your Li friends means your $1299 battery will last longer.
If you try to harm your battery by discharging it, the BMS should protect it. So a nominal 48V battery (at about 50% charge) can be charged to 54.6V (4.2V/cell or a bit higher) and discharged to about 39V (3.0V/cell) before the BMS cuts off power. Battery manufactures sell capacity, and optimize for advertisable capacity (range) at the expense (yours) of battery longevity. If you don't need the maximum range on a given day, put only as many Ah into the battery as needed. If you have a 20Ah battery and need less than 10Ah to do a daily commute, then charge to 50% instead of 100% or to 60% - 80% to allow for reserve capacity should there be a headwind.
If on Saturday you plan to ride until 50% discharged then turn around and head home, or are touring, then charge to 100%. You need to occasionally fully charge a battery and discharge it to allow the BMS to balance the individual cells in the pack. This needs to be done about every 50 charge/discharge cycles or about every month or two. Fully charging the battery should only be done when full battery capacity is likely to be used or when the pack needs to be balanced. To fully charge after use, if only half the capacity is likely to be needed the next day, is battery abuse.
The problem is that cheap battery chargers that most systems come with won't allow you to select the maximum voltage the battery is charged to. Because battery manufacturers specify a maximum voltage the battery can reasonably be charged to, even though it shortens battery life, makers of chargers use that voltage, and if you don't like it you can stick it in your pipe and smoke your battery for all they care. What is needed is a charger so smart that it does what you tell it to do. Fortunately there is one: The Cycle Satiator from Grin Technologies. And, no, I don't get a commission if you buy one, so don't bother telling them I sent you.
If you get a premium battery charger, what battery would compliment it? Price does matter, so I'd suggest the best deal is the best battery for a price that can reasonably be justified by what you're getting. There may be more premium battery offerings than I know of and certainly more than I've tried, so I'll just mention my choice: naked AllCells . And, no, I don't get a commission......
Lithium batteries lose capacity over time, starting from manufacture date, so don't buy a spare and put it on the shelf. Buy a battery with 20+% more excess rated capacity than needed so that when its capacity is 80% of rated capacity, it will still be enough. A big battery providing 50% of needed power 95% of the time, and only charged above 50% - 80% when needed will be a long-lived battery able to provide full capacity the other 5% of the time. Or use two smaller batteries to save on carrying weight 95% of time and store one at 50% SOC in a cool place until needed for the 5% trips, and alternate.
Batteries are the weak link in e-cycle system tech at this time, so optimize to compensate.