Your hardware needs really depend on what exactly you are trying to do, how big your budget is and what your current setup in your building is. It sounds like you are moving into a new place with a single ethernet connection, the rest of your place is not wired for ethernet and you want access throughout the house without running wires. This is how I will base my equipment recommendations, so if you have a different plan then let me know.
Assuming that you have one immobile computer that will act as a gateway. If you are just trying to get connectivity to a single, immobile or portable computer then I would suggest getting two cards and running an ad-hoc link between the two. If you plan to have multiple computers in addition to the immobile gateway, all mobile, within the building, then an AP and cards for the individual computers is the best way to go.
If, however, you do not want to use a system as a gateway and would prefer a wireless router to handle the gateway duties, then you will need the wireless router and a client card for each machine. Of course, with a wireless router you get the option of plugging into the router by standard ethernet too which is handy for computers located close to the wireless router. An AP will not typically have external ethernet ports; so make sure you get an AP-router.
Setup of wireless routers and AP?s are very easy, just like standard DSL/cable routers. Getting the clients to hook into the system can be a bit of a challenge sometimes. Just remember to think of setup as you would a regular wired ethernet connection. Don't worry about getting WEP to work on the first go; get all the machines talking to the 'net and each other, then implement WEP. Make sure that you get an AP with MAC address control so that your neighbor can't hijack your connection. It is also recommended that you not enable DHCP; this will also prevent your neighbor from ?jacking in.
Range is the only other concern. 802.11b works near the microwave level and has poor penetration through dense materials like concrete, metal, tile, appliances, fireplaces.... Most manufactures advertise 300-1000' range indoors, reality is more like 50-70' and can be as low as 30'. Place the AP in a high location like the attic for improved connectivity. Most of the AP's are now coming with removable antennas so you can add aftermarket or homebuilt antennas easily if range proves to be a problem.
Hope I answered some of your questions.
