Assuming NEPA is within the USA; not within Siberia...


May depend on the type of existing molding.

Got a pic ?

 

This is sort of modern style. The siding is still more or less flush with trim and the window gives an impression that it is recessed. This is what I like. But modern windows with install flanges makes the windows flush or even proud of the trim and the siding, which I think doesn't look right. What it looks like, there is none that is "standard", so you can do it however you like, as long as flashing is done correctly. I think you should use a drip cap over horizontal surfaces and always draining to daylight, but all depends on your windows and siding. Make a drawing and try to find a way to add flashing, not depending on stick on flashing.

 

Here is an example on the side of the house

 

Another photo

 

From the pics, That appears to be flat dimensional molding.
Assuring proper flashing, you may be able 'stack' the molding by installing
similar timber trim on top of existing (overlay).

Avoid the problems of removal and disposal of the asbestos siding.
Apply over the existing siding.

 

And the back of the house

 

I'd peel the asbestos off, repair the windows, and look at the insulation. You'll end up with a cleaner straighter installation and a lot fewer problem areas.

 

The window frame, jamb, looks traditional with sloped sill. As long as you mean to save the jamb, I think you can side around it. But such jambs, esp the sill, are usually damaged, rot, around that age. The storm window, esp, can promote rot because it is not well sealed and does not dry well. Mine sure have rots around/under the storms.
Why not mock first? Put the vertical boards or panel you plan to use. See if they fasten flat against that siding. Does the board/panel show wavy surface? If yes, you have to remove the mineral siding. Maybe you can nail the top and bottom, and nail the middle to keep the boards as flat looking as possible. It is just one story high, so it is more than possible to make it easy on yourself. Once panel is up, how can you add the trims? Does it stick out too much against the sill?
If fitments are good, you can flash by sticking a flashing on original trim, then nail another on top. Drip edge for top. Flashing butted to sill then covers ALL of the bottom. This may seem like a waste but any water is carried to day light and secured all of the material below the window.

 

Asbestos is bad when you make a dust out of it so those shingles could be removed with just a min of caution and care.
You have no room at the roof to add much to hide the new siding. I would also be real critical of old windows might be the best time to change them.
Today in a lot of place a solid surface siding like B&B want a strapping behind it for venting which again is difficult at the roof.

 

I would remove and dispose of the asbestos siding. It can be removed with little breakage but putting fasteners through it will break it up and pieces will fall behind lower work. It will be safer to wet it and remove it. Removing it, drilling it, breaking it by driving nails through it-they are all seen equally under most asbestos protocols as any disturbance is seen as an asbestos project. As a DIY project, most places exempt you from rules on contractors.

 

Even though homeowner can remove asbestos siding in most places, it still has to be properly disposed of. Can't be just put in the garbage or landfill. Are special requirement to get rid of. Need to find out what those are in your area.

 

House is in NEPA.

 

Assume that stands for Northeast Pennsylvania.

 

Yes

 

Some more pics of back of house and other side. Wood is old and it seems that where the siding now meets up to fascia/soffit on back of house will be easy. There I said it, easy and it’ll be far from easy

I do appreciate everyone’s input. The material behind the shingles is a black type of fiber board for the lack of a better term. Reason why I want to get rid of shingles is to make the house a little more presentable and some shingles are cracked and/or missing pieces

 

Thinking if I remove shingles will put a layer of that zip system down or tyvek paper

 

Those shingles shatter and you're going to have a hell of a time trying to drive fasteners through it.

 

Jeekinz,

Agreed....hope my neighbors are not nosy ;-)