A KVM switch works very well, I've used it to control four computers with one keyboard, one monitor and one mouse. But don't expect them to last forever -- they wear out eventually and you will have to buy another one.
like this one is all you need for 2 computers .,i have one and have been using it for 2 yrs or more now .actually mine is from before they had sound plug http://www.iogear.com/product/GCS632U/
also if you plan to use software you have in your first post the 2 towers will have to be networked together also ..I like that the software allow for clipboard sharing between the 2 towers ,with just the kvm and without networking this isn't possible
So would the cheapest option to add the other computer to my home network?
I guess so,not sure what you mean .i use a kvm switch ,i have a router ,i plug 2 cat5 cables from router ,one to each of the towers , i don't network them because the other tower belongs to customers of mine therefor i don't need to actually network them .