You can get 4000mAh - 5600 mAh LiPo batteries, and spend anywhere from $25 for one of the Turnigy packs from hobbyking.com, up to $125 for ThunderPower. As stated above, you *MUST* charge them with a LiPo capable charger. You also cannot over-discharge them, or they will swell up, effectively ending their life. They are garbage after that (and are a risk of catching fire if you continue to use them). Some come with Deans connectors already installed, some use bulllet connectors, some you have to add your own.
You can get a decent LiPo charger for around $50.
The Tekin ESC will work fine, as will your current motor. Newer ESCs contain LiPo cutoff settings to prevent over-discharging.