"leaning toward ductless - it's cheaper and easier."

That particular 36" range costs $5,000. It has SIX 15000 btu open burners. Why do people buy such expensive such high-powered ranges without a way to exhaust them?? And spend all that money, yet cheap out on exhaust? What happens when you fire up, say, just 2 of those 6 open burners, sending 30k btus of gas effluent into your kitchen?

You will need to duct the exhaust out of the house. Look on Angie's List for a good HVAC contractor.

If you don't want to do that, because it's not "cheaper" as you said, then exchange that Viking range for a significantly lower-powered one, or induction.

Vent outside. It's much better. Recirculating does not really do you any good; you'll end up with all the smells, heat, etc pushed back into your kitchen. If you need to, buy a less expensive hood and put the savings towards venting outside.

Unless you don't cook. (It's fine if you don't.). Then do whatever suits your budget and taste.

Filtering all the grease across the particulate size distribution, as well as moisture and odor, requires an extensive filtering system. The efficacy of those on the market may be user's nose dependent as to how well they succeed. There are some previous threads here that address this topic.

In my view, the only two advantages of recirculating hoods are compliance with some HMO or landlord requirement prohibiting an exit duct, and the elimination of a make-up air system. A possible third advantage would be dealing with an impossible interior architecture.

It is doable with some compromise in air quality but far from inexpensive.

It may cost you a bit more in the beginning but you will never regret that outdoor vent. When I added a kitchen to my parents old farmhouse the range and hood were located on the north wall. Living in a very cold climate we actually try to keep air access points on the northern side of our house to a minimum to maximize our electrical and mainly heat/AC chances of leakage. Drill a hole on the north and you up your stakes here. For those reasons I chose not to vent the hood and recirculated. Biggest mistake ever made in that kitchen. (And this was a very expensive and highly recommended hood) Doesn't matter how much you recirculated or how long you leave that fan run to clean the air it does not do the job. I clean and replace filters monthly. It makes virtually no difference. I decided this summer that if I could not locate a contractor I was going to head outside with my drill and reciprocating saw and change the venting myself. Outside vent is my very sincere recommendation. You can't begin imagine what a recirculating installation can be like until you have lived with it for ten years.

Of all the recirculating systems, the only one that I have ever remotely heard anything good about is the Vent-A-Hood ARS. There is a lengthy discussion about it in this forum.

Interestingly, you'll notice that even the manufacturer only recommends it for "light residential use".

But overall, Vent-A-Hood has a good reputation. And you can install multiple filter packs to improve efficiency. Of course the downside is, that this is not a cheap solution, and it also does take up a good amount of space, which you might not have available.