Can I learn to design and install a chimney myself?

Relax. A new install chimney is no big deal. Read the installation materials that come with the chimney support package and it will clearly tell you what to do in terms of the chimney. As a side note, on a new house install it is far easier to install the chimney and its support before you have much of the ceiling installed. I know this from experience. I used a Selkirk chimney kit and it told me exactly what I needed to do to get a good install. In my case I was installing a purely vertical chimney and stove pipe so I just made sure of the clearances they specified and installed it before I had most of my ceiling installed. That made it easy to get to the areas that needed attention like the support structure they have you build at the ceiling itself. Once the ceiling is in, building the special structures to hold the chimney in place means crawling through the attic which would have been a PITA for me.
You do need to decide what company to go with and then stick to them. A Selkirk chimney only fits parts from Selkirk and the same goes for the other manufacturers. It is not that they are not quite similar but each one uses a proprietary method of connecting one piece to the next so use one brand for the whole chimney and things will go smoothly.
The connection from your stove to the chimney is a completely separate item. Again you need to stay with a single supplier but it need not be the same one as the chimney. Each manufacturer gives you tons of information about how to use their products. I went with DVL but again all are about equal. I suggest that you use double wall stove pipe because it will make things much easier in terms of clearances to walls and such.
As far as being outside a wood stove friendly area, quit worrying. There are plenty of on-line vendors for both chimney and stove pipe products along with huge resources for a suitable stove. I bought a stove on line that was delivered to my door at no extra charge. It was up to me to get it inside and in place but compared to a vendor over 100 miles away that part was easy. I used a hand cart like you might use to move a refrigerator after I removed all of the fire brick to reduce the weight.

Take it slow, read all the instructions carefully. If you have questions, post them here or call your mfg. support line. Everything is pretty simple if you just use common sense and follow the instructions.

Google selkirk class A pipe installation guide. You should find a diagram depicting everything you'll need from the stove to the cap. Really easy to use.
I'd link to it but my phone is not cooperating.

I have gone back and thought about this install of yours. The SIP itself may present some challenges because the chimney support usually relies on a box you build out of 2x4s between ceiling joists or roof trusses. What little I know about SIPs tells me that part could be a challenge for you.

williaty said:

Typically, to do something like that with a SIP, you cut both the inside and outside skins off to the dimension of hole you need, then remove the foam from the center. Then you excavate the foam out from between the skins so that you can infill 2x dimensional lumber in between the skins. You anchor the 2x to both inside and outside skin and that produces a framed box. That's how our skylights are done.

Click to expand...

It sounds like you already have the SIP issue figured out. You are way ahead of where I would be for that issue.

You could try talking to some local HVAC companies. They install b-vent and other roof penetrations all the time. I did this a lot working in HVAC. Installing a class A chimney is really no different other than making sure the proper clearances are met per the manufacturer. You might be able to provide the materials and have them do the install. We occasionally installed class A pipe, but not often, But we did have a supply house that we got it from when needed.

I found the cathedral support to be pretty easy, just time consuming. I put mine through the front 2' right where the beams change from going parallel to the roof slope to where they go perpendicular and go out to the overhang. I also ran mine right up against the center beam. Lots of fun to locate all of that under the shingles and above the drywall, especially when I was 16' off the floor and my fingers were numb when I was outside. I just thought about the $1,500. I saved by doing it myself.

I didn't like the screws they supplied in the kit and used 2" lag screws into the 2x12s to be more secure and also I could use a ratchet drive since a screw gun was not going to fit well inside the support housing.