If you don’t need a hood fan microwave why get one they cost more and in your case serve no purpose IMO above the range is the worst place for a microwave. BTW a downdraft cooktop is never as efficient at exhausting as a hood fan vented to the outside and a regular cooktop while you are at it check out induction cooktops much better choice than regular electric

"If I do the downdraft cooktop, is there a specific clearance height needed between the microwave and cooktop, if I don't need the venting capabilities from the microwave?"

SECTION M1901 RANGES AND OVENS

M1901.1 Clearances.

Freestanding or built-in ranges shall have a vertical clearance above the cooking top of not less than 30 inches (762 mm) to unprotected combustible material. Reduced clearances are permitted in accordance with the listing and labeling of the range hoods or appliances. The installation of a listed and labeled cooking appliance or microwave oven over a listed and labeled cooking appliance shall be in accordance with Section M1504.1. The clearances for a domestic open-top broiler unit shall be in accordance with Section M1505.1.

http://publicecodes.cyberregs.com/icod/irc/2012/icod_irc_2012_19_sec001.htm

M1504.1 Installation of a microwave oven over a cooking appliance.

The installation of a listed and labeled cooking appliance or microwave oven over a listed and labeled cooking appliance shall conform to the terms of the upper appliance’s listing and label and the manufacturer’s installation instructions. The microwave oven shall conform to UL 923.

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All the over range microwaves that I know of are listed for the TOP of the microwave to be mounted 30" above the cooktop, or 66" off the floor. The bottom of the microwave would be anywhere from about 14" to 18" above the cooktop, depending on the model.

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"Maybe I will even mount a countertop microwave."

If the microwave is not listed and labeled for use over a cooktop, the bottom of it would have to be at least 30 above the cooktop. If you put a regular microwave as low as a model listed for the purpose, you could possibly melt some of the components and ruin the microwave.

The worst kitchen design mistake we made was to put an unvented microwave over our electric stove. We hope to rectify that in the next year and hopefully install a vented hood, and the sooner the better!