FTP to my Ubuntu machine kills my network
Solution 1:
There is nothing wrong with your network, it's not a bug, it's a feature of TCP/IP: let's use full available bandwith, and it saturates your network easily (router gets too busy).
You need to embrace Quality of service (QoS), read about it and configure it. There should be related options in your router. Take a look at page 28 in the Linksys E2500 user manual.
Anyway, this approach might not solve your problem because QoS rules may be applied in traffic being routed between LAN and WAN but not on traffic being switched over LAN.
My recommended approach is to limit FTP bandwidth.
If your [S]FTP client has bandwith limit option, use it. Here is a screenshot of WinSCP taken from the internet:
You can see the option on the bottom right corner.
If your client does not have such option, limit server bandwidth. I have not done that myself so I can't guide you step by step, but I can point you to a configure FTP bandwidth limit tutorial.
Please keep in mind that if you are using SCP, SFTP or any SSH-related transfer, your port will be 22 instead of 21, so you'll need to tweak your configuration accordingly.