I don't know about good support, but we had several sandles last year and dd's jelly shoes were by far my favorite! I loved that she could walk in puddles, or mud, and around the zoo and I could just wash them off.
DD had a couple of pairs of Teva's that I got on sierratradingpost.com last year. . . she loves them and they have good arch support. That reminds me, I have to buy some for this year.
Re: Rec. your toddler "play" sandles!
I have these for DD from stride rite
https://www.striderite.com/shopping/product/detailmain.jsp?itemID=1281&itemType=PRODUCT&iMainCat=232&iSubCat=257&iProductID=1281&sColor=93
I actually had these for her last year too and really liked them.
This is the second summer we've gotten these Nike L'il Sunray sandals. LOVE them. She even wears them in the pool (plus they float).