Definitely go dri-fit. I just got 3 sets of adorable athletic skorts and tops and JCPenney in the activewear dept, and with the sale and coupon, ended up paying about $10 per piece. Unfortunately, they mostly sold out over Mother's Day weekend. Playtex makes a great dri-fit bra called the Outgoer. I've been able to find it under $20 most times I've spent time looking online.
For the guys, they are wearing their nylon hiking shorts/pants, and dri-tech shirts, or their board shorts and rash guards. The boys are fine in the cheap
Walmart style dri-fit undies. Hubby is heavier and prefers the (pricey) Ex-officio brand, but he also uses those for backpacking and foreign travel. They can be washed in the sink and dry quickly to be used again. Travelsmith has a proprietary wicking underwear brand as well, and I might get dh a couple pair of those to try out this trip.
I highly recommend some type of waterproof shoe for wet rides, too. The four of us have Keen hiking sandals. Yes, they were pricey, but I ended up buying barely used ones on eBay for the boys, and was quite happy with what I got. Teva has some great closed toe water sandals as well, and they start at $50 brand new.
Note: if you do decide to try out eBay for lightly used Keen sandals - try some on in the store. Keens have a strange fit - Dh and I needed to go up 1/2 size, the 14 yo wears the same size as his (HUGE) sneakers, and the 16 yo actually went down 1/2 size. In general, I believe the recommendation is to go up 1/2 size in all or most Keen shoes. Of course, that's probably the reason I got a pristine pair of Keen Whispers for $50 incl shipping - they are normally $90-100 in shops.