Nice quilt! I haven't been brave enough to make something out of a panel, even though I collect them!
I only knew how to SID before discovering this wonderful board featuring a wealth of knowledge and encouragement. Now, painter's tape is my straight line guide. (don't sew over it---ask how I know!) I made a giraffe quilt for a recovery quilt for my cousin in the hospital. I used the 2 inch wide tape and just stitched vertically. here's a pic.

I would do, as others have suggested, vertical lines - inside the panel. I have no experience with doing 1/2" to 1" strips. I would do two inches or so, if you are using a batting that allows wide quilting space such as warm and natural. If I was brave, I would attempt to follow the lines of the tree trunks. I would use a disappearing thread on top and a thread that blends with the backing in the bobbin. I would sew on the line around both sides of the "picture frame". I would outline the squares on the sides. I would do something different on the border area outside the bird squares - maybe a diagonal strip or something that undulates if your machine has that stitch (doing that well freehand is difficult).
Good luck and let us see your result.
bkay

Thanks so much for all the great advice! Of course, vertical lines through the panel makes so much sense. I prefer less dense quilting anyway so I like the idea of 2" spacing. And it's time for me to venture into invisible thread, I think.

Thanks again, ladies, you are a wealth of knowledge, ideas, and support!

Love this idea, gentle vertical curves like wood. It eliminates the burden of getting stitching lines exactly the same across the quilt.