I'd like to upgrade my mother's computer for her. I bought it cheap but whenever she comes over and sees mine she makes comments about how hers can't run videos very well or is slow doing most things. She doesn't need be able to play games or anything like that, just needs a fast running computer that handles media well. Internet connection is not an issue and neither is the Wireless Router/Adapter. I figured I'd post while I was on it so I could pull up the info and stick it here. I'm looking for the basic stuff I can upgrade without throwing in anything fancy. I already know RAM is a big issue, but I don't want to put in too much and need to know if something else should be replaced first. Here is the stuff I know to provide. Let me know if any other info would be helpful for suggestions.
 

Microsoft WIndows XP (Professional)
Intel(R)
Celeron(R) CPU 2.7 GHz
2.69 GHz, 248 MB of RAM
 

As for a Video Card, my best guess is that this is the info:
Intel(R) 82845G/GL/GE/PE/GV Graphics Controller.
 

Monitor is a brand new flat screen. I knew it wouldn't help anything but didn't realize it would make things worse(slower) which it seems to have. Thanks in advance.

Upgrade that to 2GB RAM and she'll run things much smoother. Next upgrade would be a whole new system, haha!

another problem is video card i think , try to find a x1300/x1300pro/x1600/x1650/2400/2600 AGP around you (why iim saying around you is new agp cards costs alot and i think dont worth investment ,look used one.)

Another option is an amd 760g/780g motherboard (nice on-board video card for media ) and an amd cpu + 2gb ram if you want to upgrade motherboard +cpu +ram  but you may need to change psu too.

The ram is the big issue. That computer would actually run ok for what she needs it just needs more room to work in. You'll notice a huge benefit if you can get that up to 1gb of memory but 512mb is really the minimum to have a functioning XP pc. It is likely to be DDR memory (not DDR2) and you can pick up a 512MB stick for about $19 which'd give you 768MB total and that'd run much better. You should check the RAM type and how many slots are free first though. You might also be able to find cheap DDR ram on ebay (or from me as I have a ton of that crap laying around).

If you do decide to upgrade more than just the ram I would suggest something like an Athlon X2 7850 ($70), a $50 mobo with onboard video, and 2gb ($25) or 4gb ($45)of ram. This combo deal http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.203013 has everything you would need assuming you can reuse the PSU.