OK, let's see if we can break this down for you.
There are different types of batteries. NiCd is Nickel Cadmium. They were generally the first widely available rechargeable batteries. They work fairly well. They do suffer from issues like the "memory effect" where if you don't consistently discharge them before recharging them, they won't fill to capacity and their reliability diminishes. NiMH is Nickel Metal Hydride. These are more reliable. Less prone to the memory effect. Probably the most widely available conventional rechargeable on the market. LiPo is Lithium Polymer. These are lightweight, high capacity packs that deliver a lot of punch and are really awesome batteries. They are used a lot in electric aircraft and helis. And alot of guys are now using them in crawlers and other RC cars. They are a bit tempermental in how they're charged and discharged. They need specialized equipment to charge them appropriately or they have this nasty habit which I won't mention here.
Typically, you can find NiCd and NiMH batteries in the standard AA format which is the standard cell to use in your transmitter battery holder.
A sub-c battery is the short, fat battery that is usually used in an RC car pack. Like a 6-cell stick pack for a TC or electric MT. Those have the same properties as the AA but are a bit more robust and can come in higher capacities.
Capacity is measured in mAh which stand for milliamp hours. That is a measure of how much power they can put out over the space of an hour. So the basic principle is that the larger the mAh number, the longer the batteries will last between charges.
Now, for the receiver pack, a lot of companies make packs that will drop right into your ride. They are usually pre-assembled. A flat pack has the batteries side-by-side. A hump pack usually has 3 batteries side by side on the bottom with 2 batteries side by side on top so they look like a little pyramid. That's why it helps to know what kind of car you're putting the batteries in so we know if a hump or flat is a better pack.
OK, that's some basics. Any questions?