Memory RAM

What they do
They constitute the momory of the computer when it is switched on (memory is automatically cleared when the PC is switched off).
Quality to consider before purchasing one
Having lots of memory is certainly an important quality for modern computers. In fact, modern applications request more and more memory, and if they can't find it the operating system is forced to use its virtual memory (that is the Hard Disk), thus slowing down the speed of all functions.

Consider that adding RAM can make the computer work faster than a pc with a superior clock processor (not to mention the faster speed of modern DDR memory compared to the old ones).

In current computers (those with Windows XP)512 MB are the minimum requested to work in a reasonable way.

Be aware that sometimes there is incompatibility between RAMs and motherboards, and that the only way to find out is to use software of RAM testing like Goldmemory. In case of serious incompatibility, your pc may constantly crash.
 
The cost varies according to MB (obviously) and quality of the memory itself. Price also varies according to whether or not you purchase a memory from a well known brand (even if the performance is similar).
Brands to keep in mind (Memory Ram sale)
The choice varies greatly according to the motherboard (because of compatibility). Memories to consider amongst well known brands are the following:
Corsair, Kingston, OCZ, Crucial... and after... Samsung, Takei... (Corsair and Kingston leading by far...)