Difficult lawn
 

I need advice please for the re-doing of a lawn in the following conditions:
1) Clay soil with 1 foot of loose soil on top,deposited 30 years ago.
2) Hot,dry summers (north Italy)
3) Fierce weeds
Plot partly in the shade of trees,partly in the sun
What sort of grass should I use?I read good things about Zoysia and its group,but I have no clear idea of my own.Please cite the botanical name of the grasses,so that I can find them locally.Thanks.
Carlo