Regarding shoes and jewelry and hair, my first answer is to just wear whatever you like, because it’s your wedding! The dress is so pretty, you’d have to find a truly awful necklace to actually end up looking BAD. However, I do realize that this advice isn’t actually that helpful, so here are some ideas you might like to think about.
As has been mentioned already, wearing your hair down on a hot day could end up being unpleasant. Also, depending on the texture of your hair, it might end up getting very frizzy or greasy. You could, however, wear it down to start with, and get some kind of pretty clip to put it up with later. If any of your guests are adept at dealing with hair, you could have one of them be on call for a quick french braid or something.
Nawth Chucka’s idea of lining the straps in teal is brilliant. However, if you really like the sheer look, you could also line them with fabric that matches your skin tone, which would still hide bra straps.
Another thing to remember is that you can take off or change anything you’re wearing during the wedding, especially since your dress isn’t one that requires three people to get you in and out of! If you’re doing any sort of posed pictures, you could wear a strapless bra for those, and then change into something more comfortable and supportive for the party. The same goes for shoes. I know plenty of women who wore heels for pictures and the ceremony and changed into sneakers later on. I even know someone who had the whole bridal party wearing Converse sneakers for the reception. They got some amazing photos of their feet!
Since your wedding is outdoors, I’m wondering if you’ll need to walk on any grassy/unpaved areas. If so, you probably want to stay away from stilettos, even short ones. If I were to pick out shoes for you, I would go with something like this or this. If you don’t like these, and you can explain what you don’t like about them, we can try to find something better!
Your choice of jewelry can affect the overall look of your outfit. Since your dress is casual, you might consider more traditional bridal jewelry to balance it. Or, you could do some really fun things with the relaxed look- peacock feather or big turquoise beads or anything else you like. Was there anything you really loved to play dress-up with as a little (or not little) girl? Is there any particular kind of item that catches your eye in store windows? Some women just want to look like themselves on their wedding day, while other women go for things that they only really get one chance to wear. Do you feel yourself leaning in either of those directions?
Congratulations on the wedding, and good luck with the rest of the planning!