When I started I too pushed too hard and didn't spin enough. About 2-3 months later I am able to keep a 92-96 cadence pretty easily and it feels right for me. After getting a cycling computer you can really get an eye for those numbers - my recommendation goes to the Garmin Forerunner 305 (because I can also use it for running)

For longer rides I just bring a few Kashi bars or Nutrigrain bars. It works for me for rides upwards of 30-50 miles.

Shades are a must. I find my eyes get watery and then more irritated and red without them. I currently use some Oakley Flak Jackets, I don't think they're that great for cycling. I just purchased some cheap $30 shades on amazon for cycling that show more promise, they wrap around and have vents to prevent fogging. I bet you could look there to find quality shades that fit your budget.

I would also recommend getting some spare tubes, wheel levers, a multitool and a seat bag for when you find yourself further from home. A frame pump and rear blinkie to boot.