In my limited experience with doing DIY custom marquees (mainly for NeoGeo Minis) I'd suggest getting it printed out at Office Depot on regular color paper (as photo paper will be too thick and block light). It's cheap and good quality. Also are you using plexi/lexar in front of it? If not I'd have them cut it and laminate it. But keep in mind 2 things if you go this route:
#1 - Your design has all white borders, so you might want to expand the image on all sides (increase canvas size) and either make cut lines, or just dump a solid color on the outside surrounding it, so they have some guidelines to cut it to size.
#2 - You might want to take into consideration that if you go the having them laminate it route (instead of plexi in front of it) you want to give them room as they will leave about 1/16 an inch around all sides where it's just laminate. You could always cut this later, or have them cut it to the design, but by default they'll leave a just laminate edge, so that it can hold better.
As far as lighting goes, many purist here will tell you to go with fluorescents, but if you already have LEDs that you can spare, I'd just go with those as they'll last longer. Honestly though, Walmart has fluorescents on the super cheap all assembled that you should be able to fit to your size marquee.
Hope this helps & good luck!