The real hindrance would not be the amount of RAM, but its speed. An older motherboard might not have the bus speed to run the top end stuff today. Not a huge deal unless you were looking for monster performance, which I assume you are not if you have been making do wiht 512mb.
Also be careful not to combine your current RAM and new RAM (i.e. adding new RAM stick rather than replacing your old ones) or the newer stuff will probably be restricted to running at the same speed as the older stuff. By that I mena if you keep your current old RAM stick and just buy 1 new RAM stick to put in next to it, the new RAM stick should work, but it will be forced to run at the same slower speed as your old RAM stick since the computer can't handle memory operating at different speeds. Again you may or may not care about that, but just nor eason to waste money on a very fast new stick if you are goign to slow it right down by putting it next to your old 512. If that's the plan go ahead and just get an older/slower stick to put next to the 512 + will work the same way. To maximize your speed, you would find out what the top bus speed is on the motherboard, and then get two new sticks (I guess 1gb each in this case) of that speed.
That's not really the case. The best reason to use two identical sticks of RAM is because paired sets always internally outperform non-paired sticks due to the fact that they will undergo less data loss, memory corruption, and will always come stock with the same CAS timings.
Even if the stick of RAM in the computer right now is lower than PC3200, putting in two sticks of PC3200 mostly likely won't make the RAM run at that speed. If a, say, PC2700 stick is in her computer right now that means her CPU is running at 167 FSB, and unless s/he is planning on manually upping the FSB on her processor or applying an FBS:RAM ratio, then the effect of the speed of the RAM s/he buys is practically nil.
Although, an unlikely case could be that her processor does have an FSB of 200 and is already running on an FSB:RAM ratio with PC2700 (or lower) RAM. In that case, buying PC3200 and turning off the ratio actually
would result in quite a speed increase for the whole computer. However, these types of set ups in stock computers are rare because FSB:RAM ratios almost always end in a slower computer with more problems. They were common in budget set up computers from a few years back when DDR1 first hit the scene. It was much more expensive back then and manufacturers could lower the price of their computers by throwing in slower RAM and slapping on a ratio.
Still, I'm guessing that the one stick of RAM in arwen's PC is PC3200 and that there's no ratio set up. I will echo Bricklayer's advice and tell you to make sure you buy a paired set of PC3200 RAM. Partly because it will perform at top speed for your computer no matter what, and also because PC3200 in a paired set it is often a much better value buying some slower versions of DDR1 (such as PC2700) just because it is by far the most common type.
Also, you could try out a little program called CPU-Z (
http://www.cpuid.com/cpuz.php). If you install it and click on the memory tab and then report back your RAM's clock speed, any one of us could tell you the exact type you have in there and if you have one of those pesky ratios on or not. But, its not all that necessary, since PC3200 will fix you up no matter what.