xp or vista.?

graphics card will let you play 3d games ....onboard graphics will give a lot worse 3d game performance . If you don't play computer games such as shoot em ups / aero simulators/racing games you probably won't need one. the 4500 onboard graphics flomo was looking at does high res graphics as far as i can tell so should be ok with a large monitor , but cheaper onboard graphics may well limit you being able to use a big monitor.

do you get the hourglass symbol and lots of hard disc access at the same time a lot .....if so could well be a symptom of low memory available and the swap file getting hammered.If so extra memory could help ...assuming you have free memory slots in your computer.
If its a P4 depending on the age it could well be DDR memory you will need rather than DDR2 which is the newer stuff so could well be more expensive to upgrade (DDR is twice the price of DDR2 here in the UK).
If you are confident in taking the side off your computer , have a look and see what motherboard you have and if you have any spare memory slots.