I have used the Amsoil 10w30 Small engine formula for years with very good results.
In fact, I ran it exclusively in a 10hp Tecumseh that was on a garden tractor. Had it 10 years, traded it to my friend and it still runs well and doesnt seem to use any oil.
I would avoid 5w30 in a generator in Texas.
A HDEO in 10w30, 15w40 or 5w40 would work as well, along with SAE30.