I LOVE using a menu. It's easier for me because I can pick balloons I feel like doing, and if I get tired of those I can swap to other ones. It's easier for the kids because they can see which balloons they can expect to get, and have about 10 to 14 to pick from. Most of the time they don't ask for other stuff, so then they are mainly asking for stuff I either know how to do or want to get faster at. It's really win-win.
My menu board is a 2'x3' piece of plastic board. It's not foamcore, but the stuff that is like corrugated cardboard but it's plastic. It's white, but I think you can get black also. I got it at an art store. It can get pouring-down-rained-on and still be fine. It's also very sturdy.
I got those post-it letters from the poster section at Target, in neon colors, and I laminated the letters to spell out "Balloon Menu" which for now are just stuck on the board with masking tape. (I teach special ed so I laminate EVERYTHING, therefore I have my own Scotch thermal laminator which was <$30. It sure came in handy for this little project.)
Then I made all the balloons I might do, ranging from simple one-balloon to more complex ones. I took pictures of them, got prints, and -- you guessed it -- laminated them (so they, too can survive getting rained on). I was going to do hook-and-loop tape but I've just been using masking tape to stick 'em on the board cause it's easier to change pictures. It easily fits anywhere from 10 to 14 pictures on the board, which is still pretty good, and usually I pick out a 2nd set so if I run out of something or just feel like making something else, I switch some pictures.
Having actual photos is great, because then it looks like your version of whatever it is, because it IS your version. I'm not talented enough to wipe out the backgrounds, but I used a bright color fabric as my background, so it still contrasts to the balloons so they stand out. It ended up working well for me because I like being able to change or add to my menu, and I just do more pictures when I learn new balloons. I'm still learning so I need the flexibility as I get better at twisting.
My board is pretty big, so it can be seen from a distance, but a downside of that is in breezy weather it needs to be secured well. I can secure it to the little cart thingy I keep my supplies in (one of those box thingies with wheels from the office store) and that works great.
That's what works for me, but there are lots of cool ideas, and I'm sure you'll end up with something you will be happy with for what suits your twisting.