Get a quality KVM switch. Read the reviews before buying. KVMs come in different sizes, such as 2-port and 4-port. I have been using one for my two vintage clunker computers. To toggle between the two systems requires me tapping the Scroll Lock key twice. Make sure you get a KVM that is easy to toggle between systems without being a contortionist. I have an IOGear GC612A 2-port KVM, but I don't think they are made anymore. I've had the KVM for several years and have been quite happy with the device.
Pay attention to the types of connectors on the KVM. My KVM uses PS2 ports. I have to use a USB-to-PS2 converter for my mouse, which is USB. Be sure the cables are long enough to reach both computers.
Regarding networking, if you have only the two computers, you can configure one as a gateway and connect that computer directly to your ISP device. Configure the gateway system with IP forwarding. Add a second network card and use a cross-over cable to connect the two computers. I ran that way for a couple of years with a 486 and a Pentium I system. Of course, the gateway system has to be powered on whenever somebody uses the second system for internet access.
If you have plans for expansion, a router-switch is a good investment. Most models have both a router and a switch built into one box. The Linksys models are an example. A simple and inexpensive box will provide a 4 port switch. If new computers are possible in your future then get a router-switch that supports 1 Gbps. I have a Linksys WRT54GL 1.1, which has a 4-port 10/100 switch. When I built my HTPC, which has a 1 Gbps on-board NIC, I wanted to make full use of that with my office system, which also has a 1 Gbps on-board NIC. I then bought a D-Link DGS-2205 Gigabit switch. I connected the two 1 Gbps machines to the gigabit switch and then connected the gigabit switch to one of the ports on the Linksys router-switch. This way the two gigabit machines are connected for gigabit speeds and all systems in the house go through the Linksys. As I have a 3 Mbps ISP connection, the 10/100 Mbps speed of the Linksys is sufficient to handle internet connections.