Just my opinions here:
A bike w/ trailer is basically the easiest route to Big puppy transport. Easier to ride/store/aquire, but not a particularly exciting welding project
A sidecar is a manageable and good first project. I have seen a removable one here in Chicago. But they, and a lot of trikes have special issues (short version, they are "tippy" based on wheel base width and center of gravity variables). Try to minimize weight in the frame design and consider what doors it needs to get through and where to store the thing (garage, backyard, etc) Leaving it in the elements means rust so get lots of good photos before that!
here is a recumbent design I've seen a lot of people emulate
Organic Engines
Drumbent.com
There is also this recent thread
Something you don't often see on a bicycle
This is a much more practical project than building a trike pedicab I think. Unless you actually to want to charge folks to ride, then perhaps these other ideas will make a better fit to your needs/desires.
Two wheels is so much faster/safer/better in my mind! But it could be a challenging build for a first project.
This is all just my opinion. I wish you the best with whatever design you settle on!