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There are several things to consider and multiple variables. It is not so simple as mortar vs. not. If it ever gets below freezing where you are then the chances are that a concrete installation will fail or crack badly - depending on exactly how it is done. To use concrete, the only correct way of doing it is gravel bed, well compacted and then a 3" slab poured, leveled, screed and floated and then you would have to figure out how to install slates - probably using portland thinset mortar and then grouting and sealing the whole lot. Lots of work, lots of expense and even with proper base, drainage and allowance for controlled slab cracks you will probably get cracking.
If you were thinking of just using mortar mix for filling between the pieces then don't bother b/c it won't work or last and will be a mess.
If you have high clay or poor draining soil I would dig down 1 foot, level, compact, add 6 inches sharp gravel, compact, then a couple inches of mixed stone dust, compacted, then an inch of sand or stone dust - loose for setting slates. Put down slates, tap to set and then fill over everything with stone dust and compact and refill and compact. done. If well draining soil then skip the bottom gravel. If tough drainage area then fix and drain the area first with drains or drainage - or groundwater will freeze under it and heave it up. Keep the whole thing flat or slightly tipped one way for drainage - no low hollows for puddles, etc and no surrounding landscape shedding water to it. This will work great for you - cost the least and last the best with the least work. The hardest part is removing the sod, if you have it and moving the slate. Get a back support belt or you might never walk right again.
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