I am looking at upgrading to high speed internet / DSL but we have 3 computers in the house and only 1 is wireless capable. We've been using dial up and are fine with using the phone line. What is the best option for high speed internet via a phone line/plug in rather than upgrading 2 of our computers to wireless capable in order to use a wireless router?

You do NOT need to be wireless enabled to take advantage of broadband.
Simply run network cable to all the machines.

Or buy inexpensive USB wireless sticks:
Newegg.ca - ENCORE ENUWI-G2 IEEE 802.11b/g USB 2.0 802.11G Wireless Adapter Up to 54Mbps Wireless Data Rates 64/128-Bit WEP, WPA, WPA2

Will products like this work with any wireless router, for the most part? If so, I think it would be more economical to buy the router from my local provider than lease it like I was thinking I would do.

In my experience nothing purchased from the local provider is more economical. All wireless routers and adapters are built to meet industry standards and will connect to each other. Remember that the "modem" that comes from your ISP is their property, that's the bit that decodes the signal from their lines to your computer. A wireless router sits between the modem and the computer.
http://pigtail.net/nicholas/tp-link/router-mode.PNG
Some ISPs (like mine) offer the modem that has a built in wireless router.

Thank you so much for your help, I think this is the solution I was looking for!

I still think there should be a closed thread or solved thread option!