You should be able to connect your modem/router to any phone point/extension in the house provided that they are wired in correctly and of reasonable quality. The main thing you need to be aware of is that you must have a micro filter connected to every phone point in the house and all devices connected to the filters.
Router wise I would not like to point you toward or “plug” any specific device mealy give you some things to consider in your purchase.
For ease of configuration make sure you get a router with an inbuilt ADSL modem (and wireless AP if you want wirless), if you get 2 separate boxes it is much more complicated to configure and also more expensive.
Next you want to consider how you want to connect your computer(s) to the router. Wired network cables will function fine up to 100m and is the faster and more reliable method of networking, but you do have to run the cables to every computer. Wireless networking can be slightly more complicated to setup and there are security features that should be enabled to stop the whole street accessing your network/internet. Even with the latest “Turbo” mode 802.11g devices quoting up to 125mbps, wireless networking is in reality still slower than wired equivalents, though more than ample for sharing a 1mbps internet connection. The only reason you should need the fastest wired/wireless networking equipment is to transfer files between computers in your home.
Finally as AOL is your ISP you need to set the MTU (maximum transmittable unit) in the router to 1400. Not going to go in to a long description for this, just take my word that for performance and stability reasons this should be done.
Although I am loath to say it you may wish to talk to AOL about this, however your best bet would be excatly what you are doing ask around on the forums, different people will recommend different kit, find out what each set up offers as advantage (cost, ease of use, etc) find out what suits what you are going to use it for.
Jon & Daniel