You are MUCH better off venting through the roof - no comparison.

Ditto weissman-a ducted system is an order of magnitude superior to any ductless system.

Another vote for venting up through the roof. And furthermore, the arrangement you mention is actually better than most people's duct system in that it'll be a straight shot up, which is ideal for exhaust. Most people on this forum have to contend with at least one bend, and likely more than one bend, with horizontal runs as well as vertical.

While you're at it, make sure your new duct is a good size of 9" or 10" diameter. Don't skimp on that. You are so lucky you have the opportunity to install a duct. I myself am stuck with an existing 6" duct which is inadequate, but there was nothing I could do about it.

HIRING SOMEONE FOR THE JOB MAKES ME VERY NERVOUS. THIS IS ONE JOB I WOULD NOT WANT SOMEONE TO DO A SLOPPY JOB. BUT HOW DO YOU KNOW? WHERE DO YOU START IN KNOWING WHO TO HIRE? I REALLY DON'T KNOW OF ANYONE TO GIVE ME A RECOMMENDATION.

I would get an HVAC guy to put in the duct. I would also consider an inline blower if you have attic space above.

A good HVAC person will know how to run duct, since that's half their job anyway. You just have to know where the hood will be and what model so he can get the duct to the right place.

First of all don't be so nervous-this is not rocket science. I have installed two thru-the-roof ducts and two gas fireplace vents over the last 10-15 years and not had a leak yet. And I am not exactly a professional carpenter. Don't forgo an external vent because you are afraid to have someone cut a hole in your roof.
You need a moderately skilled, methodical handyman. Start with the store you are buying the hood from-hopefully they are not a big box or onlne. They usually have tradesmen they can recommend. They might even quote installation and give you some kind of warranty. Even if you are buying on-line try some of the local stores anyway for recommendations. Don't you have friends and neighbors that occasionally have work done around their house? Ask for references for similar type work and check them out. Are you in the middle of a kitchen renovation? The guys doing that job can install the duct. This is not a big deal. You already probably have several holes in our roof for plumbing vents and these were installed by plumbers not carpenters. If all else fails try your local newspapers; usually the kind people you need advertising in there. Just check references for the similar type job and if they haven't some something similar, don't use them. Try a fireplace store-big part of what they do is install stovepipe flues that often go trough the roof. Come summertime their install business falls off and maybe they have time to do your job.
I will disagree with heimert: don't go with a HVAC guy. They are no more skilled at cutting holes inf roofs than anyone else and they are relatively expensive. Most of what they do is hang sheetmetal furnace/AC duct. Again there is nothing complicated about your ducting-6 or 8 feet of vertical stove pipe-Don't need a HVAC person to install that

I wonder, what would the thought be on a rangehood (on the outer wall) on the first floor of a two-story house. Vent through the wall (short, but with a 90-degree turn) or up through the roof(vertical, but long)?

Bends provide extra resistance to air flow and the effects are usually expressed as additional effective duct lenght. one 90 degree bend might look like you added and additional X feet of duct to your run. And the effectiveness of your vent is determined by the overall effective length of the run. Someone else can fill in the exact numbers. But I would guess than one very short run with a 90 degree bend out the back wall is probably much better than a long run through the through two stories. I assume the hood vents out the top and the bend turns the corner to go out the wall? Whole run is two or three feet max. Go through the wall if you can-cost you a lot less to. We couldn't because it would have vented right in the middle of our deck :-(

i installed a viking hood with a 600cfm fan with a litle help from a general contractor, during a kitchen remodel.

i chose to vent out an exterior wall, using a 90 degree duct joint. total length of the duct is less than 3 feet including the bend. 7 inch duct used per man. recommendation.

the 90 degree bend was attached directly to the hood/fan outlet. The bend was housed above the hood, in some small cabinets (otherwise useless) directly above the hood. I used a miniature Sawzall (basically a hand held reciprocating saw, made by Black and Decker), to cut out the back of the cabinet, the drywall behind the cabinet, and the plywood sheathing over the underlying wall studs. This left me with just the exterior brick that needed to be cut, to allow the duct to reach the outside. I chickened out and had the a general contractor cut the brick for me (with a small handheld diamond saw), and install the vent hood and ducting, after I had prepared the remainder of the install. I also wired the hood/fan with Romex.

I think i', handy with tools, so it was some work, but very doable. the main problem is if you run into wall studs behind the drywall, that lay in the path of your ductwork. then the difficulty factor is gonna increase significantly. I was lucky, and no studs were in the way. also, the min-sawzall was worth buying ($40.00 roughly) just for this one project alone..

from what i read in the viking literature, a 90 bend in the ducting was the equivalent of adding 10 feet to the duct length (in terms of resistance). the 600 cfm unit was rated up to 50 feet in straight duct, so i was just fine...works great.

ductless is impossible if you get a high BTU cooktop and plan on any sort of searing of meat..you will set off the smoke detectors and have a miserable dinner in the smoke

So a handyman is all I really need? It sounds like a HVAC person really isn't any more skilled at putting a hole in the roof. And as mentioned they are relatively expensive. Fireplace installer guy, that seems to make sense too.

can you run the duct work to an outside wall inbetween the joists?

the motor you pick (along with the recommended duct size) will result in a "maximum recommended duct length" per the manufac. Also, addding 90 bends to the duct will "add" a variable amount of resistance (equiv. to 10 feet of duct length for my 7" installation).

again, you might ask a contractor about running the duct between floor joist in the ceiling, to an exterior wall. you would probably need some drywall work on the ceiling, some messing with the cross members between the joists, but it might be easier than running something up to the roof..depends on your layout

We are going through the roof as well because the only other option is right onto the back porch where we enter and exit 99% of the time. The trickiest part of the installation will be the collar and vent cap at the hole in the roof. Our GC will handle the ductwork, but the roofer insists on handling the roof work himself. He takes his leak warranties very seriously, I guess, and no one else is allowed to mess with his roofs, lol. A handyman is probably fine as long as he is as meticulous about handling a roof penetration as a top notch roofer would be.

DH may try this. What would be used for a cap?

I have a 3 story house plus attic. Are there limitations when venting through the roof? What are the recommendations regarding the type of blower you need for long vertical runs? Do you reach a point where the run is too long or too high or do you end up with a blower that sounds like a helicopter?

The cap is something like the link below. I'm not sure if the collar is something separate from the flashing or if they're the same thing.

Here is a link that might be useful: roof cap

I wonder, what would the thought be on a rangehood (on the outer wall) on the first floor of a two-story house. Vent through the wall (short, but with a 90-degree turn) or up through the roof(vertical, but long)?

In this case, I would prefer the wall. A bend adds resistance, but so does extra length.

All else being equal, I prefer fewer holes in the roof.

My options are ductless or go up through the roof or go through rafters of 1 car garage and out the side of the garage (longest run). So it is hole in the roof or hole through side of house (garage).
Considering having it go through the garage to avoid hole in roof.
We have a 1 story ranch with attached garage. Kitchen is by garage. The vent is a GE profile 400CFM. The stove is a electric GE Profile slide in.

What would I look for in a roof cap?

Use the one lmarletto linked to. I have used it and it is a very good product. Handles up to 8" diameter duct which is good for hoods up to 600 cfm. Has a built-in back damper and animal screening.

If DH is going to try this, just make sure the duct doesn't have to go where there is a ceiling or roof joist. If it does, this makes things more complicated and at that point you probably need to look for a handyman.