There should be a sticky on this type of stuff...

"mAh" - The pretty big number 3000, 4200, 5000, etc is the packs milliamps
Or how much it can hold. It is a factor of load over time

"C" - Is a number between 10 & 50 or even 60. It is the multiplier of the mAh ratting for instantaneous current or punch.
3000mAh x 30c = 90amps
4000mAh x 25c = 100amps
5000mAh x 20c = 100amps
5000mAh x 40c = 200amps

"S" - Is the number of cells in a pack 1s = 3.7volts, 2s = 7.4v etc
The maximum voltage that cells are at when fully charged is 4.2v/cell
Packs should be stored at 3.6-3.8volts per cell.
Balancing is also a concern in my opinion.
If you have an old out of balance pack & it is charged to 8.4v (peak 2s), & one cell is low, that means the other is likely high.
Over charging & over discharging makes the cells unstable & they can/will catch fire.

The benefits of a fancy charger is usually more possible current & voltage output & comfort features.
I have inexpensive $60 chargers, & $125 chargers... I use both types.

This is the basics, & there is a lot of little things to consider when choosing a pack.
Weight, size, etc...