It sounds like AOL is your only ISP??? I will assume that they are providing your broadband connection to the internet via DSL or Cable---sorry to show my ignorance but I have no idea who AOL is using for their broadband services.
Please check with AOL's website on this, but typically an ISP (internet service provider) provides you with a broadband connection (DSL or Cable) modem. The modem will have a CAT5 cable with an RJ45 plug(looks like a phone connection but bigger) that runs from the modem to your existing PC.
When you buy a wireless router, you will unplug the CAT5 cable that went to your PC and plug it into your new wireless router's WAN connection plugin. You will then need to buy a wireless network Card (NIC) for each PC that you have on your home network--you can have up to 254 computers sharing this internet connection(not that I suspect that you will have that many PC's at home!). Linksys makes pretty decent stuff for home users that is pretty cheap. The IEEE802.11G is a very common wireless standard that offers the benefit of allowing faster communication in between your home networked PC's--it will not speed up your internet connection over the older 802.11b.
Communication between your new router and the AOL modem will appear to AOL as the same connection that you used to have---IE they will only see one MAC address despite the fact that you have many PC's sharing the modem connection. You shouldn't need to upgrade your connection with AOL--I suspect that they want people to upgrade so that they can supply their own router and charge you more a month which just means more money out of your pocket to AOL when you can purchase your own hardware (router, wireless NIC's).
Setting up wireless security and getting all of your machines to talk and see each other is the next step, which is pretty simple but if you are new to all of this you may want to post to the site again for suggestions.
Cheers...