To transmit and receive signals to and from multiple nodes in a three-story house what type of antenna should an access point use?

You should buy an omnidirectional antenna with a high gain (measured in dBi) if you have a wireless G or B router. If not, I recommend you to buy a wireless N router that comes with 3 antennas. It really increases your signal strength and range. You don't need to have a wireless N adapter to use it, as it supports the older modulations