I'd love to have thermostatically controlled heat mats but given the quantity of trays I'd need to heat I'm not wanting to invest the money in them. I'm hoping that I still see a decent enough germination rate without them.
I found that heating mats do not seem to work very well, since they result in excessive drying out of soil. (Moisture tends to move from warmer areas away to cooler areas)
What I found works better is having an enclosure to be able to contain humidity in the air, and then having a small heat source within the enclosure. Even possibly a heat mat under an open container of water. This way the warmth and humidity can migrate to the seedlings, rather than the seedlings being directly warmed and then losing moisture to the surrounding air.
Since you have a clear plastic lid to cover it, heat mats may be able to work. But it is still going to result in much condensation.
Both LED lights or fluorescent will work equally well, and special LED grow lights do not really work any better than normal LED light. Theoretically, LED is more efficient and uses less energy, but in reality none of the energy is really "wasted" since the wasted energy all turns into heat, which is desirable in this situation. If this is being kept in an unheated room, you might even consider insulation panels that are coated on one side with reflective metal foil, to help hold in the heat.