Those 3dmark benchmarks are some pretty horrible results...were those run with an integrated motherboard video card?...if so, that would explain the low benchmark scores. Also, at first when I saw that you had a celeron I was kind of worried because in the past celerons were pretty weak...but fortunately you have a celeron D which I found out are half way decent...check the following article to see how your celeron D 2.8ghz chip stacks up against other processors: http://www.anandtech.com/printarticle.aspx?i=2093
From the benchmarks it looks to fall somewhere around the performance of an AMD athlon 2500XP processor which is decent if you don't have a ton of cash lying around to upgrade. So for this system I would think a 5700LE would be a decent match. I don't know if all those games you listed will be able to be played at 1024X768 though...a few of them you might have to play at 800X600 full screen still but I could be wrong and you still might be able to get away with 1024X768.
However if you can get the extra money then of course a new motherboard with a agp or pci-express slot would be better. The only problem is that I don't know what power supply you have and if it will be enough to stabily support a newer powerful system with a good video card...so you might have to get a new powersupply depending on what you have. Also, you'd of course be buying a new motherboard so there is a fair amount of cost there as well. And depending on the case design on that emachines...a new motherboard may go in easily or hard...or you might have to get a new case...not sure about this one. Plus, if you want to keep the same processor then you have to make sure you get a motherboard that supports that processor for sure. And then after all that you hastill have to fork out the cash for a better video card and you'll probably want to spend at least $150 to $200 on that to get at least something middle of the road. So things can start to get complicated and costly, but it all depends on various factors of course. The best thing would be to have someone who builds computer at least look at your situation and help you out and maybe they could give you some more exact advice. Hopefully I'm not bombarding you with too much info here...but when cash is tight I figure its better to have too much information when making a tough decision.