You should have no difficulty starting the nightshade plants in your new greenhouse.  If you choose to start your squash plants in the greenhouse, hold off for two or three weeks.  Alternatively, and just as effectively, you could direct sow your squash seeds around Mothers Day, or when the soil temperature is closer to 65 degrees.  Even the nightshade plants should be held in the greenhouse until the soil temperature reaches 65 deg.  If you transplant them earlier, they won't grow until the soil is warm enough at root depth, so either be patient or cover the soil with something to help warm the soil.  Heat pads can be helpful, but require very careful attention to soil moisture.  The most important factor will be adequate light once the seeds germinate and the seedlings emerge.  If your greenhouse is situated on the north side of your house, your seedlings may become leggy and fall over.  If so, either provide supplementary light or start over.