What kind of switch you need depends on what kind of signal you're switching. If you're switching between something fast, like video, you need something solid state, or something that's made to work with high-speed signals - like an RF relay. The same holds true if you're switching between tiny signals, like from thermocouples.
As to the device, it sounds like you're describing a time delay relay. Some act as delays, and others can be programmed to switch back and forth. They all cost too much for what they do, but make it up with convenience. You might look at McMaster Carr, Allied Electronics, or Mouser Electronics for one of these.
For elaborate sequencing of events, you can buy a little programmable logic controller that has a few inputs and relay outputs. You generally need a small 24V power supply for it as well. We used to use these from OMRON, but there are any number of companies that sell these. Again, all are grossly overpriced, but are usually easy to program with a PC and they tend to be bullet-proof.
If you need something a lot less robust, but cheaper, there are any number of little hobby companies that sell printed circuit boards with a processor on them. If you look in a Make-Magazine or Nuts & Volts, they'll be any number of these. Getting something with a chip you can program in Basic helps. In any case, don't depend on these little boards to gaurd the treasures of your kingdom, because a distant spark can usually send them reeling in confusion.
Best of luck,
- Mike