I used some of the post-emergence stuff last year and it did serious damage to some of the fescue in the lawn. It didn't kill it but retarded its growth for much of the summer.
If you go the Round-up route to kill it all, get the concentrate and mix your own. Those 1-gallon premixed things are very expensive for what they cover.
If you are going to kill all, you should probably start the process in late summer for a fall reseeding. You can rent a slice-seeder so you don't have to till the whole lawn. Tilling the whole lawn will stir up a lot of weed seeds and cause them to germinate.