If your old router isn't required from your ISPs part. Aka that you have to put it in bridged mode before the router (usually just applies to DSL and Cable connection but not fiberoptics. Looking at your router it looks like one for fiber optics.) I'd still advice checking with your ISP if the linksys is their router and is required for your connection.
You could pull a network cable from your new router to the old one and use it as an access point and that way buy a router with gigabit capacity but maybe with a little bit weaker wifi while still getting full coverage. However, it might be more expensive in comparison to buy a long enough network cable and it does require a bit more jiggery pokery to get it to work. There's also other ways of converting it to a wifi repeater but this is the "safe" way of doing it.
If you already have an ethernet cable to the other side of the house but want the gigabit connection to where said cable is, you could put a gigabit switch behind the "repeater" to avoid the bottleneck.
As for throwing a switch behind the problem would still be that the router has to do the routing, the switch would just act as extra ethernet ports and still bottleneck.
Just throwing it out there as an idea on how to get a decent setup for the least amount of money, however a good router is always a good investment..
If your only question was what router is a good purchase, I might not have been of much help. Just trying to give you some ideas on how to configure the connection and what to do with the old router.
Edited by Vicin, 16 March 2018 - 07:18 AM.