Hi, and welcome to DaniWeb.
The laptop says it comes with airport wireless 802.11n. I have been reading reviews today on line of wireless routers, and most of them are much less expensive than the Apple Airport Base Station or Extreme Station. First, are there reliable wireless routers out there which will work just as well with the Macs without spending the money that Apple charges? If so, please recommend one.
The Airport routers are a bit overpriced, in my opinion. Your Mac should work with just about any standard wireless router. I recommend using some sort of Linksys wireless router, they tend to be fairly good quality and are much more affordable than the Apple wireless routers.
Secondly, I receive dsl internet through BellSouth, and if I understand this right, I would plug my connection line from BellSouth straight into a wireless router and then both of the computers would receive the wireless signal. Is that correct? Or would the external modem still be a part of this process?
I don't know your connection, but most likely you will still need your modem. Usually an external DSL modem like the one I have translates the high-frequency digital signal received from a phone line to a regular Ethernet cable. The Ethernet cable would then be plugged into your router.
Thirdly, my husband and I usually stay at Marriott chains -- Fairfield Inn, Courtyards, Spring Hill Suites, and I have been looking at their set-ups in the room. I have seen where a guest just plugs an Ethernet cable into the wall or into something on the desk. I have also seen a note that a guest could secure a card to plug into the computer from the main desk. Will I have any problems with taking the laptop on the road and using it in my room with any of these set-ups?
An Ethernet cable should work fine. If you have to plug in a card, you'll be outta luck. The Mac laptops sold nowadays have long abandoned PCMCIA and whatever other card types are available nowadays.
Finally, I have heard of people who drive by a house or live nearby a house with a wireless connection picking up signals on their computers. Will the router I buy have a firewall to protect from this?
It will come with a firewall, although that isn't quite the right terminology. What you're looking for is actually encryption. There will be several different types available on most routers, although beware that any kind of WEP encryption is very insecure and can often be cracked in less than a minute. WPA encryption is much more secure.