Hmmm. Post Falls. You're in my general neck of the woods (we're about 40 miles north of Spokane). I start pretty much everything indoors early, but I do have a greenhouse. I just planted pepper seeds and will probably start my tomatoes in a week or so. I'd hold off on the squash, though. It grows so fast that the plants can get a bit unwieldy by the time you can set them out. And you CAN start corn indoors. I've tried it (but the seeds need to be kept very warm to germinate) and had reasonable success. I started them in 3" square peat pots and then planted them pot and all. But, like squash, they do grow pretty quickly once they start.
I start everything in good quality potting soil (I like Black Gold--Miracle Gro potting soil is way too dense and soggy) in those little 4 packs, then transfer them to 4 inch pots when they get a little bigger. The tomatoes usually end up in gallon nursery pots before the weather here permits setting them out.