Just remember to buy good batteries, this is the one place that you don't want to take any shortcuts in vaping. The last thing you want is a cheap battery that doesn't perform well, and worst case, could be dangerous. Make sure that you are getting authentic batteries, there are a lot of clones out there.
I'm not sure what kind of battery you have right now, but I highly recommend the LG HG2 (3000mah) or the Samsung 25R (2500mah), they are exceptional 20 amp batteries. I get most of a full day of usage in the eVic-VTC Mini on an LG HG2. The Sony VTC4 and VTC5 are also exceptional, but at 30 amps, they are pretty much overkill in that mod. Make sure that any battery you get is rated at 20 amps or above. I also don't recommend the Efest batteries, even though they are kind of popular and a little cheaper than most others. Efest tends to use cheaper cells and their ratings have been proven to be over inflated in the past.
Make sure you get your batteries from a trusted source like
http://liionwholesale.com/ (really popular source here in the forums). Don't ever get batteries from Ebay or Amazon, the presence of clones there is VERY high. If you are getting batteries from a local shop, ask if they can guarantee that they are selling authentic batteries, although even that isn't perfect. Many shops are ordering from suppliers that claim authentic, but turn out to be fakes. I got a couple of AWs at a local shop that swore they were authentic, but turned out to be clones. When I brought it to their attention, they immediately refunded me and found a new battery supplier (although NOT all shops are that responsive).
BTW ... It's very unlikely that you damaged the battery if you used it a little before charging it fully. You can get a lot of good information on battery safety and usage in the "battery junkies" forum here on VU.