1. Most people use PT100 type probes or thermocouples. There is no excitation voltage required for these sensors, just wire them per the wiring diagram of your controller (see 2 below)
2. I would assume a PID controller (and since you are asking get one with auto tune). There may be a special gas controller but I doubt it. Check out auberins.com
3. I am not sure what you are asking? The valves you want are 24Vac controlled.
4. Usually you choose, you can have 110-280Vac or 24Vdc.
5. The size of the transformer depends on your incoming voltage. Then it is just a matter of ratio. If you have 240Vac in and want 24Vac out you need a 10:1 transformer.