I had a 600 cfm Modern-Aire hood venting straight out in my old kitchen. It was barely enough for an underpowered gas cooktop which might have been an old Dacor, though it was mounted a bit high because of an existing window. I now have a 1200 cfm M-A hood, also venting out the wall, and mostly use induction. It's quite a bit more power than I need (they didn't have anything in between), but does an admirable job, rarely on full, often on lowest. I don't think 250 cfm would be adequate for more than very basic things like a little boiling water, a low saute of a few vegetables, or eggs. For browning meats, boiling down stock, or frying, it doesn't seem adequate at all. Certainly not for pulling from the oven. I have Gaggenau ovens, and I love them, but I sure do smell what's cooking! Perhaps the filters trap grease or other particulates, but not smells! On the rare occasions I make a bad smell (i.e., something spills and burns), I do find that my big, overpowered hood, which is about 6-8 feet away, does help. On top power. As in major suckage. Doesn't completely do it, but it helps. They used to make special hoods for wall ovens, but they don't seem to any more. I looked. I have a place to put one if I ever find one. :)

It depends on the route and local labor costs. Cutting a bigger hole, is hard to do neatly. Call a HVAC pro.

Thanks Joseph. I did not know what it actually did. trying to look at everything possible to figure this out.

Regarding hitting your head -- most people do not. We seem to have an inherent "sense" when something is close to our head. If not, you develop it quickly. I do know that we don't hit our heads on ours. My family ranges in height from 5'10" to 6'7" and we're all fine with the 24" deep hood. (It's mounted 30" above the cooktop.) In ranges, the cooking surface isn't the entire depth of the range -- the oven doors stick out farther than the cooking surface. So, 24" should cover the cooking surface plus a couple of inches in front (which is what you want). IF this were an island or peninsula installation, then a 27-inch depth would be needed since you would need extra space beyond both the back & front of the cooking surface.