Ideally you should go 36" if you have a 30" hood. (says the woman who is putting a 36" hood over a 36" induction cooktop...hanging my head in shame. LOL)

You can get an under cabinet hood, but find one that has enough power so it's not useless.

I gather wattage isn't the right way to describe cooking "power?" I wasn't sure of the terminology. I will look around, but we are limited cost-wise. As it is, we are probably spending 4x what we would spend on a basic gas range just to get induction with controls in front.

Many, many homes have the practically useless over the range microwave / vent combo. Very few of us are gourmet cooks. Amazing how our grandmothers did not die of kitchen fumes:) I have a 390 cfm vent hood and it works fine. It is small potatoes compared to what most on this forum have, but much better than a microwave / vent. My house smells fine and there is not grease all over my cabinets.

Getting a slightly bigger hood is a good idea if possible, but again, your average homeowner has the same size hood as range and the bigger hood does not always have a bigger vent inside. There are many things I'd like to have with all the bells and whistles, but sometimes its not practical or necessary.

Size is important and cp and Sophie are correct about 36” being the preferred size for a 30” cooktop. Jh is correct in that most homes have the same size cooktop and vent hood. As far as size is concerned, you do the math. You decide whether losing 3” of cabinet space on each side of the vent hood is worth it for better ventilation/capture. To me it is. Maybe it’s not for you.

Just so you know, fitting under a cabinet doesn’t mean a vent hood is powerless. Under cabinet hoods are one style, and the style of ventilation you choose depends on many things including your layout. Power here is determined by the number of cubic feet per minute (cfm) the vent hood moves. More isn’t always better. Once you cross into 600+ cfm territory - especially if you have a newer home - you have to consider the need for make-up air. If you’re budget conscious that’ll be a deal breaker. Stick to the 400 cfm category, check your local code (which is usually clear as mud), or discuss this with your contractor before you buy anything.

We have the exact kind of cooktop and cooking style. I did exactly what Sophie suggested for the following reasons. I wanted the quietest hood I could find with baffle filters and no air-ring fans. DH would not agree to an in-line fan in the attic. Those requirements eliminated a lot of hood options. The Imperial hood I ordered uses a 635cfm fan as it’s starting configuration, and I expect to never use it on full power. If I do, I will open the kitchen window in my 1980 split-level. The 36 inch hood is a positive for me, and I gladly gave up 6 inches of cab space. My last kitchen had a 30 inch hood, andI hate feeling “scrunched” when I cook. I am looking forward to those 6 extra inches of breathing/moving room even if it is just visual.

Get a real hood with power. Every time we cook now, massive smoke and smell hits the entire house. Why? I'm using a cast iron pan to sear and cook my fish and meat with as little oil as possible. Bacon? It smells all the way up the 2nd floor and through every bedroom. Slow cooker - same problem.

All this is because our hood is not yet installed. I did not realized how much smells and smoke my old hood was responsible in making the house livable. It was 1200CFM. Now our clothes smells of food all the time and they're in a walk in closet. It's amazing how smells travel.