Does my concrete patio need to be attached to my home's foundation?

I would avoid number 1 especially if he wants to charge the most, because it sounds like he's going to do the least amount of work. I don't know how stringently they enforce building codes in Houston, but if you have to get a permit from the county or city to do the work then they will have the final say on exactly what should be done for the project to meet building codes. You might want to see if you can talk to a building inspector that works for the permit department and see what they say you should do.