You said " Do I want rebar or reinforced cement poured ". Not sure what you mean - reinforced cement usually contains rebar?

Not familiar with frost heaving problems in zone 7, but if this is one large slab, and the pergola is sitting on the slab, I don't see the need for footings.

I would ask these questions of your two concrete contractors, as they have actually seen your project, and could speak with more knowledge. If I understand your question regarding reinforcement, are you asking whether it is okay to use the grids of welded wire mesh instead of rebar? In California conditions where it doesn't freeze, the welded wire mesh is more customary, unless the concrete needs to support heavier vehicle loads, in which case rebar might be specified, but this is also contingent on soil conditions and whether you have expansive soils to deal with.

The question of whether an expansion joint is desirable is difficult to really answer without having a better idea of what you are intending to pave with the slate, will it also span and cover the existing concrete paving that abuts this new pour? You might also want to ask if it would be appropriate to drill into the existing concrete patio where the two will abut, and dowel in connecting rebar between the two concrete slabs, especially if there is any likelihood that they might change grade relative to each other over time in your conditions. I don't know if base rock/gravel is usually preferred in your area, but it wouldn't hurt to ask if it is, and whether your conditions may require compacting and leveling the existing subgrade before they do the form work for the concrete.

It might be a good idea to incorporate a thickened depth of concrete footing and install metal post anchors for your intended pergola as part of your concrete work. Wood posts will last much longer if there is no earth to wood/concrete to wood contact, and the posts are bolted/nailed to metal post anchors set into the concrete.

I bet if you add a photo of your intended project, you might get better answers to what is appropriate.

Madtripper and bahia, sincere thanks for your thought provoking responses. I will try to use some flags to mark the lines of proposed patio and post pics.

I'm convinced others have had or will have similar problems, and that collectively we will benefit when told how the problems were resolved.

A third contractor came over yesterday, one my city uses for sidewalk and curbing. "I won't say the concrete won't crack." Man, that didn't instill confidence! Also said the soil wouldn't need power tamping after digging out to establish proper grade. And that I could choose to use the steel mesh (or not) or have a fiber additive mixed at the plant for strength.

Sorry, I don't want to burden any of you with too much to read. Will ask the first two contractors to return and discuss my concerns. BTW, soil here is heavy clay, but don't know if fill was brought in when house was built.

Arrgghh, and thanks,
Rosie, in Sugar Hill, GA