Growing seeds in an unheated garage

I am fairly new to gardening and am trying to figure out how best to start seeds indoors. I really don't have room for all those trays sitting around for a long period of time. I have a detached, unheated garage where I could set up a shelving/light type system. If absolutely necessary, I could probably have the trays in the house to stay warm until they sprout and then move them into the garage under lights. I am not sure if this will be warm enough for them to grow well. If I am going to need additional heat once they have sprouted, I might as well go ahead and figure out some way to heat them anyway, so they could probably sprout in the garage. I am really uncertain how to get started or what to expect. Am I heading off in the wrong direction altogether?

I am also concerned that I may have waited too late to get started. Having never done this before, the whole thing snuck up on me.

Here's what I plan to start from seed:

Moonflower

Morning Glory

Larkspur

Bachelor Button

Petunia

Dianthus

Texas Bluebonnet

Basil

Thanks,

Angela