Im not sure of brands of tanks, but a generic 48x18x18 would fit (wil a 1/2 " lip over each end) I personally built my own so can really advise you on that. (are you in the UK or US btw??)
Yes, i wouldnt use any kind of undertank heating/heat rocks due to thermal burns. Its not worth the risk. A proper lighting set up willgive them the best heat/UVB anyway so they shouldnt be needed.
Again i would rethink sand. If you are getting a baby not only do they lick everything, causing a very high risk of impaction, but it harbours lots of bacteria and parasites which may infect the baby. You can never clean up all of the poop and bacteria thrive in such a warm place. A much safer option is the carpet, or ceramic tiles (not the shiney kind, the textured kind, like slate if you can find it) as it keeps the nails trim and you can easily remove it and clean/disinfect it.
By incandecent lights, i assume you were talking about the heat or UVA bulb?? If so than yes, the normal household bulbs (not energy saving) are perfect for basking/heat bulbs. As for UVB you need a seperate bulb, such as the RepiSUN or the Arcadia 12% if in the UK. Do not get the reptiGLO or and coil/compact, and studies have shown them to be dangerous for beardies. The reptiGLO's have undergone some minor changes but the studies have been done to asses the saftey as yet. Most likely the duff ones will be sold in shops for a good while yet any way.
As many real plants are toixc, and they can raise the humidity of the tank and increase the rist of respiritory infections, fake plants are always better, but if they do start to nibble, you may have to remove them.
If you go over what you already have atm and where you are, we might be able to come up with a list of ccesities and where to get them from x x