Heyas Cat,
Almost all ecig batteries are rechargeable unless the ecig itself is a disposable, to the best of my knowledge. If you bought a starter kit, I'd think it came with a charger. So when it runs out, just recharge it. If it wears out, you'll need a new one. Most ecigs, except mods, come with a custom battery that you can't just buy at radio shak or whatnot, so you'll have to go back to the store you bought your ecig from or another such store, or buy it online. Online is a much better option, imo.
You mentioned ego-t batts in your heading. If you have an ego-t, the batteries are definately rechargeable.
Hope this helps!
Live long and vapor
Maximillian the Vaguely Disreputable