Technically, Bridge Mode is the correct setting for your Time Capsule......since you only want one router on a home network, and the Linksys is already providing that service.
That is why Apple's software configured the Time Capsule to work in Bridge Mode.....it correctly detected another device upstream acting as a network router and set the TC up as a "bridge" to avoid the two routers on a network dilemma.
If you try to configure the Time Capsule to act as a second router on the network......which is what the "tech" folks seem to be suggesting, you are going to see a message pop up to the effect that you already have another router on the network......so the Time Capsule needs to be in Bridge Mode (to avoid having two routers on the network)
Apple gives you an option to "ignore" the message, but as to whether things will work this way or not, I cannot say. One of the things that you will have to accept with type of setup is a Double NAT. That may slow browsing some or not at all. Sometimes some sites will load while others do not.....Double NAT can produce some unpredictable results. Things may work...or they may not.
I advise users to avoid the Double NAT if possible, but sometimes it cannot be avoided. If you want to try it, you'll have to change the setting for Router Mode from "Off (Bridge Mode)" to DHCP and NAT.

On the 5GHz issue, by renaming the 5 GHz, will that stop it from any interference with our internet set-up?
Probably not. Changing the name is not the same as not having a 5 GHz signal at all, which is what you were asking about. The Time Capsule cannot provide just a 2.4 GHz signal without also providing a 5 GHz signal.
In the Airport Utility, under the wireless tab, then wireless options, do I click on the box for 5 GHz and name it?
When click on the box that will automatically add "5 GHz", (without the quotes) to name of your network. So your Network Name will be 2.4 GHz and your Network Name 5 GHz will be the 5 GHz signal. You can point devices at either network to connect.
Also, do I leave the 2.4 and 5 GHz on automatic?
I do, but other users swear by trying to manually choose a channel, so there is no right or wrong answer on that one.