My understanding is that it is the second set of leaves you are looking for before planting out, that the first ones are just the "starters" (cotyledons) and that the second set are the "true leaves". This second set will look more like the leaves on a mature plant than the first ones will.

After that second set, in the ground the perennials go. They are happier there, as long as you can be reasonably sure slugs or rabbits or deer won't eat them. The tender annuals I would wait for after the last frost date.

Nan's right. Perennials can be planted almost any time after you get the second set of leaves. It's best to do this early rather than later if you can. They'll grow more in the soil than in the containers. Annuals and frost tender plants should be protected until the last frost has passed. You can plant them out, and use the tops of plastic bottles as a cloche if you want. As soon as my petunias are up, I'll be doing that. I've had friends saving water bottles for me. These are the 16oz bottles. I'll just cut the tops off, throw away the caps, and place them around the newly planted petunias to protect them for a couple more weeks. I only sowed the seeds a few days ago.

Question: I just learned that when the soil is wet you could compact it like cement. If I am able to get some perennials in the edges of the garden where I don't have to actually step on dirt, and the ground is still very spring wet, is that OK? Or, do the plants need to wait till the spring-thaw wetness is gone? I might have some true leaves before the ground is dry. I am not only very unfamiliar with the dirt in this condition, but also very unfamiliar with this detail of my climate as I've never had to worry about it before.

From what I read on the web, even digging in spring ground that is too wet can ruin the soil structure for possibly years. There is a test where you take a handful of soil in your bare hand and make a ball. Drop it from waist height. If it crumbles and breaks apart, the soil is probably dry enough. The link below explains.

http://www.organicgardening.com/feature/0,7518,s1-3-81-1431,00.html

Here is a link that might be useful: Spring soil

Second to what Bev said.
I don't remember the reason, but everything I've ever read says not to work the soil when it is wet.
Of course now someone will up and say they always work the soil when it's wet and it is fine. :)

but that's what I read, and I go by it.

It also depends on what kind of soil you have, but the general rule is to leave the soil alone when it's wet.