I sure blew it with this decision! I had the GC's plumber install the rangetop, he didn't come with the gas supply line and I spent a couple hours tracking the right one down and driving to get it. I had the appliance store's guys install the built in fridge and ovens, they damaged the cabinets.
I'd advise you to talk with the installer in advance, and review the specifications for your appliances (have them printed and ready). Also review whether there are particular issues, like a pocket door or water pipe behind appliances into which screws should not be drilled. Double ovens are heavy, no one person can "easily" install them. You didn't mention the fridge. If it is built in, consider whether you can easily shut the water off if there is a problem or leak. Good luck!

Thanks for your feedback, kksmama. I will make sure I review the specs with the installer in advance.
Our fridge is not built-in - the appliance delivery guys pushed it into place on the day they delivered; the rest of our appliances are in their boxes, in our garage.
So do you think I should go with one person- the GC recommended by the appliance store? He has fixed rates for each appliance.

Ovens and other built ins are best installed by the cabinet person, as the cabinets may need to be altered to fit correctly. However, a genuine GC (licensed and insured) with finish carpentry skills can probably do it all without having to split things up between the trades---as long as the rough ins are in the correct spots per the manufacturer specs. You need to study those, and be sure that they are correct since it sounds as though you are the GC on the job as you are hiring the trades directly.

I'd be inclined to go with the person recommended by the appliance store. I'd expect somewhat of a price break on multiple installations done on the same day.

My first choice is to always go with the installer recommended or furnished by the appliance store. This way, if there are any warranty issues down the line, there is no finger pointing as to "it wasn't installed properly"

My GC and one of his crew installed my cooktop, Venta hood, wall ovens and refrigerator. They had to had to add a little metal trim at the bottom of the oven because the height of the opening was about an inch too big. You would never know they modified it. The garbage disposal and dishwasher, air gap and soap dispenser were installed by the GC's plumber
The installation of my appliances was not actually listed on my contract but they just did it as part of the job. Their was no extra charge for it. The GC did a great job.
If you are the GC, then I guess I would go with the recommendation from the appliance store. You could ask then for references from other appliance customers who have used that general contractor.

Thank you, all!

We went through Lowes for the cabinets and countertops but bought all our appliances elsewhere. Lowes installs only when customers buy from them.

We'll go with the appliance installer recommended by the appliance store. Thanks again!!! :-)

I'd go with a GC to avoid everyone finger pointing at the other guy.

For example, if the GC/homeowner has authorized a 2cm top on standard cabinets, some slide in ranges can't be lowered enough to sit just above the top without inverting and altering the appliance feet. An appliance guy is going to be very reluctant to do that. If it's a remodel, the existing electrical may have to be moved too.

I got a call from a homeowner wanting a 3cm granite backsplash cut to accommodate a new microwave; the Lowe's installer wouldn't do it. I told him to not cut the stone, just install the microwave in front of the splash. So it's an inch proud, big deal. It isn't worth the hassle, risk, and mess of cutting the splash.

A good GC knows all this stuff in advance and knows who should do what and why.