It all depends on what kind of game you're playing. "Online game" doesn't really narrow it down that much. It could be anything from Flash based Solitaire games to MMORPG games like World of Warcraft.
If it's the former, you're unlikely to see any real benefit from a video card that you couldn't get for far less by simply adding more RAM. Video chipsets, like you tend to find in HP systems, carve out a chunk of system RAM for their own use. So, if you got a system with say 512MB of RAM, with 128MB of that going to the video chipset, you effectively only have 384MB of RAM. Adding another 512MB or simply maxing out what the system can handle will improve things quite a bit.
If it's the latter, then you may well benefit from an actual video card. If you aren't a big gamer, I wouldn't recommend getting a top end card, but you will want it to be PCI-E. For one, there are very few PCI video cards made anymore, and most of those wouldn't be much better than what you've already got. Just look at the ads for some of the local electronics/computer stores in your area, and pick out a card that's within your budget. I'd personally say go with nVidia GeForce based cards, mostly because ATI seems to have tied all their drivers to the annoying .NET Framework. I'm hoping the AMD merger will cause the reversal of this decision at some point.
As for the power supply issue, I'd try it with your current one first. If you're not a big gamer, and aren't playing a highly graphics intensive game, you might be able to get by with what you have. If you start suffering spontaneous reboots, particularly when you're playing a game, you can always go and get a new power supply. Any ATX power supply should do the trick. If you go with a cheap no-name power supply, be sure to go way in excess of what you think you'll need, since cheap power supplies never deliver anything close to their advertised capacity. If you go with a good brand name, such as Antec, I'd still go 50-100W over what is recommended, just to give yourself a bit of a buffer and some room to grow.
Finally, if your new system came with Vista, you'll want to make sure you've got at least 1GB of usable RAM for the system. If you get a dedicated video card, you can reclaim that 128MB, which will help, but all that Vista eye candy is going to want lots and lots of RAM. 1GB should be considered the minimum amount if you want a usable system. Might want to go to 1.5GB, if your system will support that much, and the games you're playing are along the lines of World of Warcraft. Most new systems will probably only come with 512MB, which isn't enough by a long shot for a usable Vista system. Especially if 128MB of that is being diverted to the graphics chipset.
I just bought an HPa1730n desktop with 128MB onboard video and a 300W power supply. I want to install a dedicated video board and wonder what to do (I'm no fount of technical knowledge). I have 3 vacant PCI slots and 1 vacant PCI-E x16 slot.
1. Would a dedicated 128MB card be much of an improvement? I'm not all that much of a gamer, but some of the online games I do play run pretty slow.
2. Where would I start having power supply issues with a 256 MB card (I'm not willing to spring for a new power supply)? The PCI cards I've found don't require a bigger power supply, but some of the PCI-E cards require 300W as a minimum but recommend 350. I know PCI-E is a newer, faster bus, but would PCI be OK if I don't need much?
Any input would be appreciated.