Hi, seaking, and welcome to ECF!
The t3s should work just fine on your battery. As far as "best" coil resistance, that's largely a matter of taste. a 2.2-ohm coil should give you decent battery life, but you might prefer a lower-resistance coil. You can just get replacement coils in a couple different resistances and see what you like. If you are getting leakage onto the battery make sure that the coil is screwed in tightly to the base! (It can tend to loosen up, particularly when you put the head back on the battery).
If you only have 1 battery, you should get a second one, as a backup and for something to use while the other one is charging.
If you're looking for something new (in a battery) I would suggest you check out the Innokin MVP.
As far as heads go, the evod's aren't a bad choice. Lately I've been preferring these:
https://www.fasttech.com/p/1594202
https://www.fasttech.com/p/1640900
But there are a ton of different clearo's to choose from, top-coil, bottom-coil, dual-coil.
Not to mention rebuildable heads like the Kayfun and friends ;-)
Fasttech has a lot of different types of clearos for cheap, so you could order several different styles and see what you like the best. Takes a while to get here, though, so in the mean time grab something locally!