Hammer if done that way...I would have to do the wood sill first...then drywall sides and top then install the J trim and mud?
Or I guess drywall first and compensate for the mdf?
I can only make the sill from 1/2" material due to window crank handle at bottom on sill.
So...If I said no to drywall and just did boxes...do you install piece at a time or pre build actual boxes with Kreg screws?
The window fits in what is known as a rough opening, (RO). This is larger than the actual size of the window. When the window is installed, it is, more or less, centered in the RO. The measurements from the edge of the window to side of the RO will vary. You cannot just attach any type of extension jamb directly to the side of the RO, it will need to be shimmed to stay in line with the actual window.
Rather than build extension jambs out of wood, a common method is to return the drywall to the window. In this case, shims are attached to the sides of the RO so the drywall will line up straight with the window jamb and account for the different measurements. Jamb edges are roughly 5/8"-11/16", so, shims that are placed flush with the backside of the window jamb work to leave about a 1/8" reveal around the window perimeter after 1/2" drywall is installed. The peelable L channel is placed on the edge of the drywall and fits against the window. You then flat tape against the L channel. After the mud is completed, you peel the peelable part of the L. This leaves a nice tight, straight line. It's the modern alternative to flat taping. Mud won't crack since it's not actually attached to the window. We use it on timber frames where drywall goes against a beam that will surely shrink.
You can drywall the entire extension jamb, top, bottom and sides. Use the normal outside corner bead where the extensions meet the wall, mud it all, prime, put on one coat of paint. Then make a paper template of the sill you want, transfer that to the sill piece, cut and install. Some only do the top and sides, install the sill, then use an apron molding under the sill. This is the easiest way to do a wood sill with ears and returned drywall extension jambs. The apron molding allows some wiggle room that will be covered. You see this method everywhere, medical, dental offices, motel rooms, just look around.
Casement windows have short turn crank handles available. Normally there is quite some distance from the RO sill to the inside perimeter of the window, unless it's an all metal window or something unusual. You can make the reveal at the window sill anything you want. In other words, if you leave 1/8"+- at the top and sides, you could leave 1/2" at the bottom and not be noticed because it's a casement. A word of caution, pros know this but others often make the mistake of cutting the drywall flush with the RO sill. A 2 1/2" apron molding may not cover this, we always leave the drywall up about 1 1/2" at the sill, it can be trimmed later as needed.
If you make the extension jambs out of something like plywood, solid wood, etc, you build a box to fit, then install that as a unit. Some do it piece by piece but it's much easier to make a box. You place shims to align the box and fasten through those into the sides of the RO with finish nails. You didn't say what the house is made of, fastening to stone is different than wood. I would not recommend using MDF. Difficult to fasten on the ends and edges, surface can puff with finish nails, heavy, needs priming and sanding, may need several top coats, will swell with any moisture, miserable sawdust and smell. You will pay dearly in the future for the small savings MDF gives today. Use birch plywood, not Baltic birch.