Older Base Station Use With HP Laptop, without a Mac?

I could buy her an old Base Station on Ebay, I just need to know the oldest model number/nomenclature that will work with a PC running XP without a Mac present after setup.

All AirPort base stations (oldest-to-newest: Graphite, Dual Ethernet (Snow), & AirPort Extreme Base Station) are based on the 802.11 standard. The two oldest only support 802.11b, and the newest supports both 802.11b/g. So, depending on the wireless capability of the laptop, it shouldn't have any trouble connecting to any of these. (ref: http://docs.info.apple.com/article.html?artnum=107908)

1) If it will work with the HP laptop but no Mac there at her house.

Yes, but her laptop will require the AirPort for Windows software if you plan on doing any administration of the base station from that laptop.

2) Can I set the Airport up for her there with my Mac laptop, then come back home? Leaving only the HP there to access the internet wirelessly through the base station?

Yes.

3) And bring my white 2001 iBook to work with some other wireless router I will buy (maybe an Airport if I can afford it), without loosing the settings for my mom's base station should I need to manage it at her house sometime in the future?

Yes.

4) To re-ask #3 above, how would I manage and remain intact the setup/management information of two separate base stations at two different sites with one little ol' iBook?

Within the AirPort Admin Utility you can create multiple AirPort configurations and apply them when desired.

"1) I just want to clarify that your confirmation that connection the connection from HP Laptop to internet will work through the Airport Base Station via dialup phoneline (I assume the HP wireless card sends info to the modem in the base station, that sends it to the dial-up ISP)?"

For the AirPort Extreme base stations that have the built-in dial-up modem, yes.

"2)Is the Airport for Windows software installed on my iBook to do admin/setup on the Base Station? Or is the software installed on the PC laptop?"

You will want to install the AirPort for Windows software on her laptop ONLY if you want to be able to administer the AirPort from that laptop.

3) RE#2: If the Airport for Windows software is to be installed on the PC, what Base Station model began shipping with software (same cd or different cd for pc/mac) to install on a PC?

Actually, I'm not sure, but you can easily download the software from Apple @ http://www.apple.com/support/downloads/airport41forwindows.html

4) What other questions am I not asking to select an appropriate model to purchase from eBay a base station to work with mom's pc over dialup?

Make sure that the AirPort Extreme base station is the model that has the built-in modem...model M8799LL/A (ref: http://www.apple.com/airportextreme/specs.html) Although the earlier Graphite & Dual Ethernet (Snow) base stations have modems, these are relatively "old" by computer standards and may be troublesome.