1> the Cisco Access Points are all connected via Ethernet. Any of them would be capable of conencting to a network served by DSL or Cable Modem (Modem --> Router ---> Switch -- AP (and other PC clients).
With some Small Office / Home Office devices (like a Linksys), some of the functionality is integrated (Router & switch combined, usually 4 or 8 ports).
2> Yes. One AP and a couple wireless NICs would be a good starting point. Security-wise, WPA-PSK (PSK = Pre-Shared Key) is a pretty good bet, or WPA with LEAP (using the AP as the RADIUS server). WPA provides dynamically generated keys, with the (desirable) option of rotating the keys periodically to keep them less-guessable.
3> Wireless standard won't matter from an operational standpoint. A= 56Mbps on a 5Ghz radio, G= 54 Mbps over a 2.4 Ghz radio, B=11 Mbps over a 2.4 Ghz radio. You will probably get better distance using "G." A "G" radio will also downshift to accommodate a "B" client (since they're on the same band).
If you are in an area with lots of 2.4Ghz devices (cordless phones, wireless video, etc), then the "A" radio would probably be better, but they tend to be a bit more expensive.
Good Luck
Scott