Unfortunately no! It is not possible to record one program and watch another if you have a single converter box. The best option is to get one box for each device. It is also ideal to have one antenna for each device. See antennaweb.org for the best antenna for your area. If the antenna signal is strong enough, an antenna splitter can be used. If you have more than one converter box in one room or close to each other it best to get them from different manufacturers so that each uses a different remote. That way if somebody changes a channel on their box it doesn’t affect you. Instead of purchasing a converter box you could buy a Digital TV. They have their own tuners so you will not need the converter box.
COST SAVING NOTE !!
You can keep you cost down by trying the equipment you have before you buy anything. Don’t let people talk you into anything. Your old antenna may be good enough. If you have have Cable or Satellite TV you don’t have to do anything. This is only for those that still want to use antenna along with the old TVs. You do not need a converter box in that case.
Suggestion
If you don’t understand any of this ask around. Many people have already made the switch including me. You shouldn’t have to call any experts here. There should be somebody that will help you get set up. FREE !! or pretty much so.