Hi there! Just a word of caution about the 55 gallon tank - If it is a regular 55 gallon tank, it is actually going to be a bit narrow for an adult beardie - they are only 12 inches wide! If it is a 55 gallon breeder tank, then you're all set. Otherwise, the 40 gallon is just fine for most fully grown beardies. As for lighting - quick run down is this:
1) You need a Reptisun 10.0 tube
UVB light. This should be mounted under the screen in an under cabinet fixture, easily and cheaply obtained at Home Depot or Walmart, or some such store. You can use 3M command hooks/strips to mount it. For a 40 gallon breeder, this should probably be a 24 inch bulb and fixture. Much cheaper to order this bulb online than to buy it in a store.
2) You need a basking light of some sort. This should be a bright white or clear light, not a colored or "daytime" reptile light. I currently use a 75 watt Zoo-Med basking light for my 40 gallon, but need to get a dimmer as it is just a couple degrees too hot on the basking spot. You can also try a 75 or 100 watt household incandescent bulb.
3) If the cool side isn't getting warm enough, you could try a 40 or 60 watt household light bulb to increase the ambient temperature.
4) Overnight you do not need any light. If the tank temp falls below 65, you will want to get a ceramic heat emitter to raise the temps. You can use a lower wattage one to just slightly raise ambient temps (which I do now), or you can use a thermostat with a higher wattage CHE to keep the temps in a certain range (which I have also done).