I haven't yet seen, though, any posts that make suggestions especially for field schools that take place in an urban, public setting like a living history museum. I also haven't seen a round up of especially women-friendly gear. So, I thought I would put together some tips for my incoming students and others.
First and foremost, as others have mentioned, most excavations will have complete sets of tools and equipment available for field school students and volunteers to use. Strawbery Banke will provide field school students with their own dig kits. However, many people like to buy their own trowel and break it in over time. The best is Marshalltown, and I prefer the 4.5" pointing trowel. If you choose to get your own trowel, make sure to sharpen it up and personalize it somehow so it doesn't get lost. (I've seen wood-burning, spray paint, nail polish, etc. -- I just put my initials on the end of the handle with a Sharpie.)
Also important are a good pair of work gloves. The best I've found is from West County and these are on sale! They are great: they come in bright colors so you don't lose them, they come in women's sizes, they're machine washable, and they even have a terry cloth thumb for wiping sweat off your brow. Best of all, they hold up really well to months of screening and they protect your hands from historical artifacts that can be dangerous for bare hands (e.g. broken glass, rusty metal).
As for clothing, I found that I had to update my field clothes drawer a bit when I moved from contract archaeology to museum archaeology. When I'm talking to the public, I like to feel presentable by wearing something other than an old tie-dyed t-shirt. Our guiding principle at my last job was to dress so that it wouldn't be embarrassing if grandparents showed up for a surprise lunch date. I like a button-up shirt with built-in sun protection (like those made for fishing) or a polo shirt. You can go for Strawbery Banke maroon, or stick with a light color to stay cool.
Pants depend on the job. Archaeologists who spend some of their time fighting briars with machetes might prefer the standard Carharrts. I've always liked those convertible/zip-off pants so that I have the option to zip-off and stay cool or to zip-on and keep my knees clean. I prefer a lighter color so that ticks are easy to spot. Lately I've found a few pairs that have built-in sun protection or insect deterrent, or both! Regular shorts, leggings, or jeans are also fine. You do you.
Shoes depend on the job as well. Sometime rugged hiking boots or steel-toed boots are needed or even required. For a museum field school, though, sturdy sneakers or hiking shoes are fine (I like low-top Chaco or Keen shoes). Waterproof shoes are extra good for bailing out a test unit after a rain storm. In general, you're looking for something comfortable that won't make you feel clumsy on site and that will protect your toes (no sandals).
Perhaps the most important thing to wear on site is sun protection! Hat, shades, and sunscreen, sunscreen, sunscreen. Reapply after lunch. Bring a reusable water bottle and fill it often. Gear, your trowel, notebook, and lunch (never get separated from your lunch!) can all be stowed in any old backpack or bag.
Above all, be comfortable and ready to share your exciting experience with museum visitors. Archaeologists, am I missing anything? Comment below with tips or your favorite outfit.