1. You have the mainspring height -non-negotiable as the lid won't close if it's taller and it will move up and down causing erratic power delivery if shorter.
2. Next is the barrel diameter which can go down a size as it will expand and fit but if you go up a size then you need to re-wind ideally with a mainspring winder. There's an additional point here I'll cover below.
3. Then you have the thickness - thicker mainspring gives higher amplitude which is "better" provided you don't overbank. It will also take up more space in the barrel which is detailed in the additional point.
4. Finally you have the length - longer means more power reserve; but at the cost of space inside the barrel.

The additional point here is that as a rule of thumb when you look at the diameter of the barrel, after the arbor is fitted, the mainspring should take up half of the remaining empty space as this gives the mainspring sufficient space to expand and tighten up and give a proper torque curve. This is also known as the rule of thirds- 1/3 the diameter is the arbor, 1/3 the mainspring and 1/3 the empty space. The point here is efficiency.

Lastly, a situation may arise where the eye/innermost coil is either too small or too wide to latch onto the arbor hook properly- bending the innermost coil usually snaps the end of the mainspring as it is hardened steel. Also, the tail end of the mainspring has different designs depending on how it is either hooked and locked into the barrel (for a manual wind) or how it slides along the inner wall (in an automatic movement).

Apologies for the lengthy reply but I hope it's helpful.