I have this hat: http://www.rei.com/product/732926 and I love it. I needed something that's packable, not straw or other mesh-like weaves, and that has a strap (it's sometimes very windy). It's up to you if it's cute or not, but thought I'd suggest it. I loaned it to my mom last year and ended up having to buy her one too.
I spend a lot of time trying to find sunscreens that won't aggrevate my eczema, and also protect my fair skin. I don't have acne but have rosacea issues (can look like acne) with certain ingredients so I'm very careful with my cosmetics etc. and rarely use 'mainstream' stuff anymore. Both my parents have had bouts with skin cancer so it's something that I take quite seriously.
So far my Ok (no burn, no breakout) sunscreen list includes: Vichy, La Roche-Posay, Avene, Biotherm, Blue Lizard, California Baby, and Badger. Some of those rank well on the database, some don't, and some aren't even in there. Avene doesn't break me out, but it is hard to spread, and Badger is highly scented FWIW. Some people also like Vanicream for it's low EWG rating, but it made me break out almost immediately. Here in Canada we have easy access to the French sunscreen brands that use minesol so I've been using them for years; I only recently tried CA Baby, Blue Lizard and Badger.