Alright dorn I will jump in. From 2015-2020 I worked in new concrete and concrete repair. I was mostly on the commercial side but spent 20-30% of my time on residential in the DFW area.
Our business was to try and repair cracked or settled concrete flatwork and home or building foundations by using polyurethane injections to lift flatwork and the interior of buildings and use piers to lift footers and stem walls. We also ripped out and replaced items that were beyond repair. We had our own concrete crew in house and worked with subs on things like flagstone and pavers.
I have been to more than a dozen homes with failed flagstone patios (wet or mortared style) and there is no repair option. This was in the DFW area with expansive clay soils. The mortar beds were plopped on top of a few inches of sand or dg, but it was useless as tits on a bull.
When the soil moved, the mortar bed has zero structure and it popped the flagstones up creating death traps. If you do flagstone and there is any type of risk of movement from tree roots, erosion, expansive clay etc, you have to do on top of a reinforced (#3 rebar 18" on center) concrete slab 3.5" thick. The other option is to dry fit it in sand so if you get movement you can reset it like pavers, but everyone of those I have seen is kind a mess of sand getting tracked around because the gaps are so wide in flagstone. I can't imagine sealing it holding up for long either.
The three primary options for grade level of patios in order of expense are concrete, pavers, and flagstone. Pre Covid pricing on a concrete patio your size in DFW with reasonable access would have be $8 per sf for a simple broom finish. You can dress it up by mixing a color dye into the concrete in the truck for $1 a square foot and do a salt finish for another $1 per sf if you want it to look a little more unique.-- I did this exact option on my pool deck. Pics below.
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Pavers should not be that expensive in the south honestly and are my favorite option for a non structural patio. I'm doing a paver project myself this summer. 450 SF and its up against a retaining wall with several angles that have to be cut. Where I live is ridiculously expensive for construction (new builds are pushing $500/sf.) I was sure I would be diy on this project, but I used my old hack of going to the supplier and asking for a competent small paver contractor that doesn't advertise. Guy quoted me just under $14/sf which is $1-1.5k more than I would have paid to do it myself after renting a dump trailer, saw, laser level etc. His work is great according to the yard.
Flagstone, done right would have to be in the $25+/sf range imo, because you need that structural slab underneath. So it's effectively a concrete and paver project added together.
So all that said, I would go find a couple of different paver suppliers and ask for recommendations for competent young hungry installers. I would guess most times pavers are sold by contractors (like myself back in DFW) that hire these young hungry guys as subs and mark it up 40% to the homeowner or buy companies that drop tons of money into overhead and advertising. No way you should pay as much in the south for pavers as I am in the mountains where we are 2 hours from suppliers and our build season is from May to October before the snow comes.
Also, ask for the cash discount after the quote. These guys really like cashola.