Sprinkler system with Spherical holding tank

I live in West Seattle and I'm an accomplished DIY. I'm thinking about putting an irrigation system in my yard so I can water my grass. I would prefer not to use city water to do this so I'm leaning towards using an underground spherical holding tank that would collect my roof's rain runoff. I'm not sure on how big of a tank I would need or how I would hook up my sprinkler system to it?

I've researched NORWESCO tanks and the 300 gallon under ground tank with pump platform looks like the solution but I'm not sure. My roof pitch is 6/12 and its square footage is around 2500. My lot size is around 5000 square feet and maybe 2300 of that would be considered my yard. Would a 300 gallon tank do the job? Would Seattle's rain be able to fill up the tank so I would have enough during Spring and Summer? If so, how do I hook up the sprinkler system to it so the pump can provide the lines with water?

It's the thought that counts. Now you can let it go. 2300 sq ft of yard can easily drink up 5000 cu ft of water in a season, and that's over 35000 gallons.

I have a 1/2 acre lawn. When its 90 plus degrees outside it uses roughly 1600 gallons of water a day. Your lawn is much smaller, so assuming a similar light clay like soil type you would need 177 gallons a day. Sandy soil will require significantly more. I don't think the savings you would realize by using rainwater would offset the cost of just using city water.
-rick