You need a footing regardless of frost in order to lay stonework. Putting up stone from the footing up the wall is by definition a veneer -- what I'm hearing you say is that you don't want thin stones pasted on. Good choice!
Your location and frost depth will dictate the depth of your footing. I would pour your footing when you pour the slab. You'll need to lay your stone up from the footing using wall-ties nailed to stout underlayment and framing every foot or so as you lay up your stone. You will have problems with the wall flexing and cracking your joints if you don't.
It's not hard and actually fun but you have to do it correctly. Also use a vapor barrier between the stone work and the underlayment (can be tar paper). It is counterintuitive but using 6" - 8" stone is easier to lay than using a narrower vener -- less cutting and fussing.
For your laying mix, use 3 parts course sand, 1 part Portland cement and a half a part of lime to mix your morter. Mix it dry-ish -- damp acutally (clumps well but will not cream or bleed) and lay no more than 3 feet vertically in a day. Scratch your joints back about an inch and a half after the day's work and when completely finished laying stone, point the joints using a pointing trowel and a morter mix of a finer sand and a little more lime than previously. Again, don't make the morter wet -- should be much much less wet than brick morter. Every two or three hours, when the pointing has started to setup, take your pointing trowel and cut the edges of the joints where the morter meets the stone in order to clean up the joints and take off the "curl" from the morter caused when you pointed the joints. When pointing, do not over dress the morter. Each time you smooth-out the morter, you bring more cream to the surface which can cause a mess. Always point into your previous work such that you pack it in tight to the previous work. When the pointing is crumbly, use a wisk broom and gently brush the joints to remove the very top layer of the cement revealing the sand in the pointing mix.
After a week or so, acid wash whe whole wall with a stiff brush and muriatic acid diluted in water but wet the wall with water first and rinse everything carefully afterward.
Should look stellar.
