Ask ten drummers what they’re looking for in a snare drum sound & you’ll likely get ten different answers. The usual descriptions often come up "Fat /Big" etc., but when one digs beneath the surface, especially if one has been doing this for a while,those replies can get very detailed. I think that with few exceptions,"Tone" is relatively high on everyone’s agenda & while we (hopefully) all agree that there’s no substitute for a great touch, having a basic handle on not only the ability to tune a drum well but to understand the effect different heads have is important. It’s worth spending a few minutes reading up on the different characteristics.
For me & the snare drum sound I’m after, it’s usually a 300 Opaque on the bottom & a G1 Coated or Power Center Reverse Dot on top. I’m learning that the drum is the thing that makes the different sound ; occasionally I’ll "Amplify" a snare’s tendencies with an appropriate head - for example an EC2 coated or an ST Dry on an (already)dry-sounding snare, but typically I’ll put on the heads listed above. What’s important here is consistency from head-to-head ; if you have two supposedly identical 14” batter heads that simply aren’t ( like some manufacturers) your reference point gets blurred.
It’s also really important to get decent snare wires. I use Puresound and they have a staggering array from which to chose (dry / wet – wide / narrow) so you can take that snare drum further in the direction it’s already headed. And if you haven’t "Got This" already, be very careful how you actually set the wires up. Too close to one side or the other &/or with only the slightest twist [ on the horizontal plane ] & you’re not making the most of your investment !
Finally, to re-iterate, how you strike it is probably more important than anything - & that doesn’t mean “ how hard you can hit it “ either. Good luck !