I'm really not sure. I have 2 dell computers, one has the dual video card which enables me to have two monitors to the one computer the other cpu only has the video card for a single monitor. I have the split cable that plugs into the back of the computer with 2 separate connectors, one for each monitor. I need to be able to do the same thing with the other cpu, I want to use the smaller one for storing all my pictures that I take and the bigger one for school etc. I need to be able to run both computers at the same time if I can also, I have a splitter that will enable me to hook up both cpu's. I am way new to this, I always had my IT guy to work this stuff out for me before I got laid off, now I'm on my own.
Most video cards (even the cheaper ones now) can support two monitors out, especially if you're not going to be doing much gaming on them.
If you need to connect two computers to the same monitor (and can use the same keyboard and mouse), you need a KVM (Keyboard Video Mouse). You probably won't find many that will allow 2 monitors out, but certainly can find a variety that will allow you to have one monitor out for those two computers.
Please look up DMS-59 and see if that's the connection you are looking at - Dell had a line of computers that they used this connector and had a cable that would allow you to plug in 2 VGA or DVI monitors out from the one connection.
Based on what you are detailing your uses for these computers, why not just use an external hard drive for your pictures and not use the second computer at all?