Remove sod, roto till 3-4 inch depth, put down a bag or 2 at the most of lime, level, roll it, seed it, roll it, water it, enjoy it.
I would use top quality topsoil and very little mulch. Mulch generates too much heat for some lawn seed while it is decomposing and it will shrink up while doing it.
I would not hassle with a water system for such a small area, but that is your call. These are great for most peoples needs,
http://www.amazon.com/Nelson-Raintrain-Traveling-Sprinkler-1865/dp/B00002N6AN mine is over 10 years old and going strong with auto turn off.