I've never tried to grow a plant
before. What I'd like is:
1. a small indoor garden, perhaps on one of those wheeled shelves in the garden
department.
2. lot's of flowers that perhaps I could rotate to my kitchen table and back.

It will be located in a room that receives the afternoon sunlight, most
likely in front of a sliding glass door.
I live in Washington State

The list you presented are all outdoor plants. They will not survive indoors
for any length of time, although you can use the indoor garden to germinate
seeds.
You don't mention fluorescent lights, which could be used during the winter to
supplement natural light.
Your biggest problem will be heat buildup & low humidity when the sun is out.
If you want flowering plants, start with a few African violets. Don't forget to
rotate them regularly to obtain symmetrical growth.
Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)