Use the sun as much as possible. It is brighter than your lamps and most seedlings will love it. Watch out that you aren't frying very small or sensitive plants.

Mushrooms usually mean it is too wet. 60F is a little low for germinating many plants, and even a little low for growing on some. The low temperature is good for the mushrooms. Different plants need different amounts of water, but for most veggies and annuals you should let the surface of the soil dry out between waterings after they have germinated. Before germination, it is best to have the soil moist but not wet and to cover the trays in plastic to keep up the humidity. If you can get the water right then I think the temperature is OK.