John... just had a quick scan through but yes your PC should be fine... where you would notice an almost immediate improvement though would be in memory... I'd highly recommend you bung a further 512mb in it...
According to the Crucial Memory configurator HERE you need DDR memory but you need to make sure it runs at the right speed etc.... (PC3200 or PC2700) would be OK. Your PC apparently has two slots so one will probably already have 256mb in it but it is possible that two lots of 128mb have been fitted. As I say stick another 512mb in it or maybe more.... your PC can apparently go to a maximum of 2 x 1GB memory.
Doing this will make a huge difference to the speed of you PC... memory isn't expensive and even cheaper off the net/Ebay
If you want to get into Online games then my personal opinion is to get a Xbox 360, there are plenty of strategy games.
On the broadband front I hate AOL and always have... do they still insist on you using their crappy browser and used to be strict on sharing a internet connection with other PC.... frankly I think you could probably get much better. I have cable but do use ADSL (via a telephone line) in the office.... I have absolutely no complaints with https://www.bethere.co.uk/ - cheap, fast and extremely reliable, definitely worth you considering in my opinion.