check out irrigationtutorials.com for instruction. But you'll have to calculatate the GPM per dripper and basically depending on your size of your system split it up into zones.
Drip tape might be a good idea if you have row crops, but if you're targeting individual plants, individual drip emitters are my preference to get right at the root zone. We had gigantic plants with our drip system, 2-3 emitters per big tomato/pepper plant.
Rain barrels typically are useless unless they are huge, i.e. thousands of gallons in a location where you don't have city water. Think remote site with a pond a hundred feet away from the rain barrel. Basically, you don't want to go there, it's a wasted effort, use it for spot watering or making Compost tea etc... but realistically it's not a feasible option if you have city water. The pressure of rain barrel is typically so low that you would need a pump or a separate low pressure system, i.e. low pressure drip tape etc...
If you have your beds pretty heavily planted, I would say just rough estimate 20x20 would be as large of a zone as I would do... I had roughly 40x40 area in our last house on 3 seperate 1/2 drip lines, and it worked... no calculations, just seperated by different types of plants, i.e. raised beds on one, perennial beds in the sun on another, and roses on a 3rd. Personally, I would just split your 50x50 section into 4 parts and go from there, use drip end timers and call it a day. Just make sure to use a backflow preventer and good filter off of the main supply. I got a 4x hose splitter and that got me 3 hose end timers + a garden hose, with the filter ahead of that. Backflow preventer highly reccomended ahead of the filter!