Decks, Patios, Porches and Docks - Patio design/Ideas

Hi all, I'm new to posting to the forum but have been reading your many great posts for some time now. I currently have a 200 sq foot concrete patio that needs help and I have a few ideas I'm milling over. I want to add some sort of slate, flagstone or tile to the existing concrete patio to add appeal. I plan on doing all of the work myself and will be doing a mortar/grout application to the existing concrete depending on what type of material I go with. My first question is, in with Missouri whether would anybody recommend laying tile on an exterior patio? The patio is half covered (under a deck) and half exposted to the elements. If so, what kind of tile?

Second, if I decide to go with flagstone, any recomendations? Ideas on cost PSF?

Any other material recomendations?

I don't want to stain the patio unless I have too. In other words, unless the cost element for the flagstone/tile get's out of hand.

Thanks in advance for all of your advice!

I don't think the slate or flagstone will hold unless you are going to raise the height of the patio at least 2 inches. A thin layer of morter under it, isn't enough. I'm not sure about the tiles either. You could brick it instead. That would look nice.