Bennet Springs is a great park, here are my suggestions. Aside from fly's you need to fish a light leader and tippet. A 9ft 6x/3lb test leader and tippet will work. I even use 7x/2lb test tippet when the fish are picky. As far as fly selection I like to fish small. Size 14,16,18 in Pheasant Tail Nymphs or Hairs ears under an indicator work. Scuds in the same sizes tan, gray, and olive in color under an indicator. Midges also work well in size 16,18 black and red. Adjust your lead shot according to the current and focus on getting a clean drift with your setup and you should do fine.
I also suggest fishing in Zone 2. I think the water has a few more features that make it more fun to fish but zone 1 is great as well. If your there for the weekend I would dedicate a day to each. I'm far from an expert but I think that will get you started. I'm sure some others will chime in and help you out. Good luck and have fun!