Home network router or switch

Most modems supplied from ISP's are router/modem/wireless combos which have 4 ports at the back. If you need more a switch is all that is needed for more ports.
Since you did not state what your existing equipment is ,all I could offer is a general reply.

Multi port routers (past 4) are rare. I owned an old SMC 7008ABR which had 8 ports, but it was more or less a freak of design... Typically if you need more than 4 ports you would add a switch to your network. Try to keep your internal LAN on the switch, and then uplink to the router.

Typically, your SOHO network would look like the following...

ISP Connection
|- Modem, cable, DSL, FiOS, whatever...
|- Router, WAN port on the router connects to the LAN port on the modem. Sometimes, most commonly with DSL and FiOS I believe, the ISP provides a modem / router combo unit. The router provides your network address translation so your ISP provides one IP address, and your router allows you to share it with all of your computers and devices on the network, it also typically provides a local DNS service, firewall, Wireless connectivity, sometimes media streaming or NAS services etc... The router really is more or less the service gateway between your network and the internet.
|- Switch. Yes many routers have 4 ethernet ports, but that is often not enough. For my home network for example, I have a 16 port switch, 1 port on the switch is dedicated to uplinking to the router, the rest attach to the computers and devices I have that use wired ethernet. Make sure your switch has enough capacity to provide all the ports you need.
|- Client devices. Workstations, servers, game consoles, whatever connects to the network are more or less last in the chain.

If your telephone wiring is structured with cat 5e, yes you can reuse it, just terminate the ends with one of the normal wiring standards. Look up RJ45 wiring standard and you will find a variety of sites that show you how to terminate those wires.

Don't go back to the telephone distribution block though. In your central location add a patch panel, or just terminate the cat5e with RJ45 plugs, and hook up to your switch.

As I mentioned above, there are a few 8 port routers on the market, but the wired gigabit speeds are 10/100, you wouldn't be able to take advantage of gigabit speed wit them. You would be FAR better off getting a quality router with 4 gigabit ports and tacking a gigabit switch on behind it. Especially if you plan on doing things like streaming media, VoIP, file sharing etc...