Heavy gauge strings and a solid steel definitely improve sustain.
I think the damping of the strings behind the steel with your trailing fingers is also important for tone. I think this anchors the strings and stops them rattling against the steel.
I bought my steels from elderly.com Here are a few pics. I admit to being a bit showy - the first pic is on with my 1936 Gibson lap steel EH150. This is first pickup made by Gibson - about the 180th or less in serial sequence. Its called the "Charlie Christian"
Left to right, the steels are: Shubb SP1, Lapdawg, Bob Brosman bullet. There is also a nut extender to right it clips over an existing nut for temporary conversion.
Dave Gilmour used the strat on his lap with the "bullet" type steel. Peter Green says he played his part in "Albatross" with a strat on his lap. There's enough pedigree there to not need to worry about whether its right or not.
I have some resources on lapsteel instruction / technique. Let me know if you're interested.