How do I hook up Time Capsule if I leave that the same way, or do I run iMac via WiFi?
Plug the Time Capsule (TC) WAN port into the main router by ethernet.
Then plug the TC to the iMac with second ethernet cable from LAN port.. or wifi is also an option.. but ethernet is always the better, faster, more reliable choice. For the actual setup however keep wireless turned on.. it is not quite but almost essential. IPv6 in the computer should also be set to link-local only if you have issues.
With this physical setup run the airport utility in the Mac and it will configure the TC for you in bridge mode.. which is correct.. you can also use the TC wireless with the same name as the Uverse or different.. that is up to you.. if you setup the TC far from the Uverse.. then running both devices with the same wireless name and same security settings/password will give you much better wifi coverage. On the other hand if the modem and the TC are sitting alongside each other there is no need for both to do wifi. Generally I would therefore recommend the Uverse wireless be turned off.. but there are exceptions where you might want guest wireless.. in which case the uverse can provide that with a different SSID.
Purchased Time Capsule to use a s back ups for my iPad, iMac, iPhone, etc.
Just so you know.. the TC is useless for ipad or iphone.. Apple did not design iOS to use backup target of the TC. It is designed to backup to iTunes on the Mac.. which is then backed up to the TC.. so indirectly backing up the iOS stuff..
Or iCloud.