Why are you keeping outdoor plants in the house?

The plants started from seed sound as if they got damping off disease which can be quite common with a lot of plants started from seed. Good air circulation helps in preventing this as does not keeping the soil too moist since newly emerged plants rarely need much water. I have heard that you can put a layer of vermiculite on top of the soil and that helps prevent damping off. There are other cures out there for damping off where you make up a solution and spray the soil and plant with it. I am sure you can find quite a few by googling damping off.

Unless your temps are still cold, you should have begun hardening them off by placing them outside first in shady areas, gradually increasing the time they are outside and then increasing the amount of sunshine they get. That couldn't hurt either.

Thanks! I thought it was still too cold to move them outside for hardening off. I will try that today for a few hours and then increase their time outdoors. We've been having some pretty warm days here lately. I like the trick with vermiculite as well. I will give that a go next time.
Thanks for the advice.
As for the other two I lost...they were outdoors. I may be new to this, but I'm pretty sure I know an indoor plant from an outdoor one!

I agree that it is damping off. Most Clematis are hardy down to zone 5 so likely not too cold to move them outside.