I'll try to explain everything you need to know...
First and foremost, you need a radio system. It's best to get the best possible if you know you are staying in the hobby so you won't have to spend extra money upgrading in the future. Something like a stock turnigy 9x is perfect for beginners and experts alike (Once you get into more complicated stuff you can upgrade the filmware to er9x for more options, but don't worry about that for now)
Another GREAT radio is the dx7. Seriously consider getting one if you plan to stay in this hobby for good.
You normally get 1 receiver with the transmitter you buy, but you'll probably have more than 1 plane in the future right? This means you'll need more receivers- 1 per plane
Extra rx for 9x-
http://www.hobbyking.com/hobbyking/store/__12339__Turnigy_9X_2_4GHz_8Ch_Receiver_V2_.html
Extra rx for dx7-http://www.hobbyking.com/hobbyking/store/__11965__OrangeRx_R610_Spektrum_DSM2_6Ch_2_4Ghz_Receiver_w_Sat_Port_.html
The plane you're buying or building needs to have a power system that fits its needs specifically. Normally kits have recommended parts. If that's the case, just get what they tell you to and you'll have a flying plane.
Some don't provide what you need. You'll need to know the weight of the airframe and a general size prop. Look through some motors and look at the specs of thrust and prop size. If those meet the needs of your plane, then that is a good motor to use. KV is rpm per volt. It's important to know that higher kv motors like smaller props and lower kv motors like bigger props. A 2200kv motor with a small (6x4) prop is great for a fast parkjet. A 1300kv motor with a bigger (9x5) prop is better for slow flying and 3D. I can't cover all of the rules here though.
Now that you have a motor that looks to be good, you need a way to connect that to the rx. A speed control does exactly what it's name suggests- Provides power to the motor to make it spin faster/slower. You'll need to look at how many amps the motor draws in the specs. If it says it draws 15a, then you'll need an esc (speed control) that can handle 15a or higher. It's good to go overkill on the esc but for 15a, you don't need more than a 20a speed control.
Next you need a battery. Again, look at the specs of the motor and see how many amps it draws and how many cells it will run on for what you want. It says 15a and will run on 2-3 lipo cells. 1 cell is 3.7 volts. The more cells, the more power. So you decide you want more power and go with a 3s battery. You'll need to find a 3s lipo that can deliver 15+ amps to the motor.
This equation will help you find how many amps the battery can deliver:
A(amps)= Mah X c rating
Mah is the capacity and c rating is how fast the battery can discharge power. Say the battery is 1500mah, 20c. The equation would go like this:
1.5 X 20 = 30 amps
So a 1500mah 20c 3s can deliver 30 amps- way more than you need for the motor that only pulls 15a. If you want a long flight time go with this battery since the motor won't be pushing the battery all the time. A lighter plane can be achieved with a smaller battery (1000mah 20c = 20a) but flight times won't be as long. Never use a battery that can't supply at least the motors max draw.
Something to add about escs- Most under 50a have something called a built in bec. A bec supplies power to the rx and servos. You don't need to buy and install an external bec unless you are using more than 5ish servos.
The dx7 and turnigy 9x both have mixing built in for elevons, vtail, etc... You won't need a v-tail mixer for any plane as long as you don't use gyros. You don't need to know about all that just yet.
Ask anymore questions you have. I tried to cover all the basics you need to know. If there's any mistakes, would someone please correct me
It took a while to type all that and I'm not so sure its mistake free lol