Hi,
Do you currently have a video card? Does your Motherboard have a PCIe slot for a video card? (Suggest you post name of PC .. e.g. Dell XXX or HP xxxx, or post name/Model of motherboard and power supply.)
Yes, starting with just a video card and seeing if the PC is enough better that you enjoy using it as a good strategy.
There are two main sizes for video cards, "small form factor" cases take "low profile" video cards. The rest of the cases pretty much take normal video cards. You can get an excellent very low power video card for $100. Low power lets you continue to use your PC's current power supply.
Your current CPU is slow (1 core , 1.6 ghz). Your CPU fits in an LGA775 socket. There are some reasonable upgrade choices that do not need a new motherboard (e.g. a q6600 (4 cores, 2.4 ghz) used on ebay is about $20-$30) but the BIOS from your MB must support it. You find out if the CPU is supported by reading the supported CPU upgrade list for your PC (Dell XXX) or by looking at you MB's supported processor list. NOTE: you need to get both a CPU and a new "heat sink fan" (HSF) if you upgrade CPUs. The HSF for your low power Celeron will not work for a higher power CPU.
Aside: if you get a new MB it is not likely to fit in an Dell or HP case -- the plate that covers the IO will not line up and the connectors for the front panel IO (e.g. USB) will need work. Hacking the case to make things fit is possible, but the one time I tried it I decided just to get a new case. Not worth the bother.
Final thought... what copy of windows do you have? WinXP is no longer safe to surf the internet -- no bug fixes so once the bad guys find a new way in ALL win XP systems will be hackable and microsoft will not fix. If you need to a new copy of windows also then forget upgrading your PC. Instead look at a used complete PC with win7 or later. Something like this "..Fast Dell OptiPlex 790 MT Windows 7 Pro Fast Intel i5 Quad Core up to 3.4GHz 8GB.." for $250 is very much better than upgrading your PC, and you can thebn ebay your old PC for $20-50 or so.