Choosing the right batteries
The "batteries" you list (AAA, AA, C, D) (there isn't an "A"), are not technically batteries at all, they are "cells." But in common vernacular they're called batteries anyway. Let's dive in a bit:

A battery is actually two or more cells grouped together in series to produce electricity. A cell does this by using various chemistry. Depending on the particular chemistry chosen, a cell might produce 1.5 volts (alkaline), or 1.2 volts (NiMH, NiCd).

The size of the cell (the amount of chemistry) determines how long it can continue to produce energy. The larger the cell, the more capacity it has. Don't confuse this with voltage. For a given chemistry, a cell will always produce the same voltage.

In alkaline batteries, the various cells you list all produce 1.5 volts. The "AAA" is the smallest of these, and therefore will have the shortest life span, for a given load. The "D" is the largest.

Combining these cells in series produces higher voltages. Combining them in parallel produces higher current capacity. By capacity I am referring both to maximum current developed as well as longevity (mAh).

To power a 9V load, you can combine six 1.5 alkaline cells in series, or use the common "9V" battery. Notice that six "AAA" cells are physically larger than one 9V battery. You would be correct in thinking that, being larger, they would have greater mAh.

The datasheets for these cells provide a lot of data. The most important properties are:


Voltage
Current capacity (mAh)
Performance under load


The last one is something that is often overlooked. Let's take the "AAA" cell datasheet for example. It is 1.5V and has a current capacity of 1200 mAh. Or does it? The chart on the very first page shows four bars which depict current capacity at different loads. This means that the battery capacity actually varies depending on how demanding the load is. With a light load of 25 mA, the battery will provide 1200 mAh, or for about 48 (1200/25) hours. Under a heavy load of 400 mA, you will only get a little over 1 hour (450/400).

Knowing this, hopefully you can select the size of cell that best fits your needs. If you have the budget, the room, and no other constraints, and you want to power something for the longest time possible, select the largest cell you can.

In many applications, you don't have that kind of freedom. You said you're doing radio control, perhaps a remote control plane. That application imposes all kinds of limitations on you. The plane can only lift so much, and you might not have much physical space in which to place cells.

Everything is a trade off. Size, cost, and performance.