The 5th from the right on the bottom is bothering me. Value wise it belongs in a different place than colorwise. Perhaps remove this one??
Other than that ... swap the 3rd and the 4th from the right with each other.
Definitely keep the stripes, they give great texture to bargello as long as you cut across the stripes and not lengthwise to the stripes.
If you do go shopping ... cut a small strip (1" x 3") from each of the fabrics (even the ones you don't plan on using) and staple them together in the order that you plan on using them. You can then see what you have alongside what you are contemplating purchasing.
One more piece of advise with regard to using prints in bargello. Try not to use any print that has an area that has a color change larger than the smallest bargello piece you will cut. For example ... if the smallest strip you will cut is 1/4" x 3" long ... don't choose a print with 3" blue flowers on background that shows 3" of green. Reason being is that you are bound to run into a piece somewhere that is showing all green and no blue, thus ruining the visual "run" of blue.
It's looking good so far!!