time machine base or extreme base

There are two different basic ways to "extend" a network, with one being much better.....performance wise.....than the other.

The best way by far to extend a network is to connect the wireless routers together using a permanent, wired Ethernet cable connection. Trying to "extend" a network by using wireless to connect the routers always results in a significant drop in performance on the entire network.

Apple sums this up for you in their support document on extending a network:

Adding Wi-Fi base stations when it is unnecessary can reduce Wi-Fi throughput because the Wi-Fi network will require more data management overhead. The network configuration also becomes more complex. In the case of a wirelessly extended network, throughput may be reduced to less than 60 percent of that of a single device. The general rule is to keep the Wi-Fi network as simple as possible. You can accomplish this by using the minimum number of Wi-Fi base stations required to service the physical network area and by using Ethernet wherever possible.

Extending the range of your Wi-Fi network by connecting Wi-Fi base stations together using Ethernet is always the best option, and will provide the best throughput.

Wi-Fi base stations: Extending the range of your wireless network by adding additional Wi-Fi base stations

You did not indicate "how" you planned to extend your network in your post, and the answers to your questions will depend on your decision. Please post back to let us know how you want to proceed, and we'll offer our recommendations.