Hi, and welcome.
There are a number of programs that will work with DVD's - Nero is commonly bundled with the burners, and is usually highly recommended. Your Phillips disks should work fine.
I've never looked into burning PS2 disks.
If I were going to replace memory, the first thing I'd do is check the memory chips on the computer. Many of the chips have a large sticker that tells the size and speed of the memory. If they don't, you can usually get a magnifying glass and find a number on one of the small chips that can be searched on Google.
Seems as if a lot of Dells usually use PC2100, but I haven't seen all of them.
However, here's a site that guarantees their memory is compatible with your computer.4allmemory site
The site says PC800, so it must be an older Dell.
Remember to use Electrostatic Discharge precautions when handling memory or anything inside your computer. Turn it off, pull the plug, and either use a wrist strap or ground yourself to the case or large metal object to remove static electricity from your body before handling the memory. Don't be walking across the livingroom carpet with memory in your hand. Keep it in the wrapper until you use it.
Make sure you line the memory up with the notch in the right direction and that it's completely seated and the clips are closed.
Here's a site that advises on copying Sony disks:PSXtune
If you want to make archive copies of your own DVD's, you'll need to decrypt and shrink them. DVD Decrypter has been removed from the internet, but you may still be able to find a download site somewhere. There is also DVD43 which decrypts on the fly. DVD shrink is still available. There are legal issues about whether you can make copies even for your own use, just so you know.