The Lieutenant Governor will take over, like Perry did for Bush. Not sure about the next election.
It will be a Republican as there is little to no democratic party. I hope it will more moderate one but I have no idea who is in the running. Maybe Bill White will run again. I remember there was a Dem from Dallas who seemed pretty good that ran the same time as Kinky Friedman but not sure if he will give it another go. I think it would be interesting if a strong candidate come out of the Latino population.
The reason I harp about Perry is I think he has instituted a culture in Texas that is antagonistic to education. Not just public, but education in general. It worries me when science is such a driving force behind innovation but political leaders question its validity. I think it will worry the business community as it has already.