One plane can usually be fitted with more than one kind of battery, so they are more often used for weight balancing. Personally, I prefer lighter batteries, even down to 1000 mAh, but I have flown with bulky 2000 mAh batteries and I can assure you that planes fly with those...just much faster, and in a much less controlled manner.
Of course voltage is very important, and the main thing is how many cells are strung together. Generally I fly with 3S batteries. Another important parameter is the discharge current, which is important for FPV.
This is the battery I often use, 2200mAh, 3S, 25C discharge current, around $10
I also used slightly more expensive batteries, 2000mAh, 3S, 45C, around $20
Do also store your batteries properly, as there will be consequences otherwise.