Each location provides its own unique challenges for installation of soffit and the trim to support it. In both cases there are a number of choices to make.Do Vent or Not to Vent - ...and I don't mean steam!
The choice of venting is a bit moot. You absolutely require venting for the roof - or attic. Roof venting is a total system consisting of that big vent (or more) sticking out of the roof - typically as high as you can get it - PLUS a means to get the air flowing from as low on the roof as possible. As low as you can go is under the eaves, hence, the use of vented soffit is the best way to go. And besides, most building codes require vented soffit at least on part of the eaves. I suggest for a consistent look just do it all in vented soffit.
ASIDE: It is the flow of air from the lowest part of the attic up through the highest stop on the roof that will keep your attic, and the cottage, nice and cool and take away any nasty moisture.
Illustrated at the right are 1) a vented and an un-vented soffit, and two potential profiles - 2 and 3 pane. There are many more profiles to choose from. We choose a 4-pane vented soffit profile. This gave a wide 16-inch soffit so that I did not need to cut as many pieces as each covered a lot of territory.
We used vented soffit for all the soffit we have around the exterior of the roof. This maintained a consistent look and feel tot he soffit. The recommendation from the roof vent manufacturer was that we do not install any vents in the gables - so we did not install any.
The vent manufacture also suggests that the air flow pattern is kept even across the entire eaves area by not having any air entrances higher than the eaves. Given that we installed vented soffit in the rake areas of the gables we technically have broken this rule so I may insulate or otherwise restrict the flow from the soffit in the rake area. Furthermore, we are installing 1/4-inch plywood for the ceilings of the from and back porch and the gazebo. This will eliminate huge air entrance that these ceiling area represent in respect to the other eaves. PLUS the plywood provides a much stronger surface in which to install the pot lights.
Square or Mixed
Another choice you need to make is whether to have a square or angled joint when the soffit changed direction under the eaves. (In the illustration below square is on the left and angled on the right.)
Either works satisfactorily and really is based on your personal preference. We choose the square version for all of the 90-degree corners. For the eaves on the gazebo there are no 90-degree corners so we used a modified version of the angled version. In either you need to install two J-Channels back to back to support the soffit at the joint.TIP: I have to say that I severely underestimated the time it would take to install the soffit. Soffit, or rather the supporting trim for the soffit is very tedious to install. I would double or even triple your estimates.