Thank you for your lovely comments!
The yarn is Caron Perfect Match in Cape Cod blue - I reasoned that I'd want something machine-washable if I would be toting this all around the city.
As for lining it, I actually tried doing it with my sewing machine first, and my machine was really
unhappy about that.
The bag looked like this before assembly:
I ended up cutting pieces of the white fabric, which I marked with blue chalk in the shapes I wanted the bag pieces to end up since the knit fabric was rather elastic and prone to getting out of shape. I sewed the first lining to all the knit pieces before I sewed the bag itself together. I was careful about placing the sewing thread so it would sink under the knit stitches, but as it turned out the way I sewed the outer seams of the bag covered all the sewing thread anyway.
For the inner lining (the blue floral fabric), I folded the two fabric edges over toward each other to look like a finished seam then sewed tiny top stitching at the very edges where it would be hidden by the knitting. (I think I may have photos of this part still on my camera - if so, I'll post them.)
I'm not sure if this is actually the way to line things. I basically looked at a blouse and checked out the way the lining was sewn into a cuff then mimicked it. It made a neat result, so I was pretty happy.