Congratulations on successfully avoiding the window replacement industry. There are many good, local and honest outfits out there that will do the work well, and for a fair price. However, they are overshadowed by the high pressure clowns that rule the game. I have seen them screw the elderly and unaware I my area, to the point that they were paid 10X the cost of the products they installed, and the victim ends up with an unaffordable second mortgage on windows they didn't need, and can't afford.
Now to the details. As a retired small builder, I have installed a few hundred of these. First, you have a solid game plan so far. Be aware that ALL vinyl windows are custom built, so getting the exact dimensional fit you need should not be an issue at all, if you find that stock sizes vary too much to fit your tolerance. Having custom sizes made in vinyl windows is generally pretty reasonable. When it comes to installation, I would do a few things slightly different. Caulk is good, quality is an issue. A lot of cheap, latex based stuff will dry out and fail in a few years ,and standard silicone doesn't stick to vinyl at all. The most commonly available product that will perform well is GE Silicone II, which will be labeled as usable on vinyl. Next it's fasteners. 1-1/2" roofing nails are the preferred fastener over screws. The reason is that screw heads protrude and will not allow the trim to sit flat. I nail every other slot on the flange, which gives you at least 20+ fasteners per window. The proper technique for the install is to have a helper inside the opening, with a pile of shims, and a flat pry bar (wonderbar). The helper removes the screen, opens the glass fully,then passes the window out the hole. At this point the helper is totally responsible for holding the unit until you have at least one nail on each side flange, half way up the flange. The helper keeps the unit secured by keeping a firm grip on the sash, in the center of the window, and keeps inward pressure on it, so the flange is tight to the sheathing. The helper centers the window by looking at the right and left gaps between the window and framing, just above the sill. They adjust this by using the flat bar to slide the unit back and forth. Now you level the sill. This is done by you checking the exterior lip of the sill with a level. Your helper uses the bar to lift one side of the window and shimming under the corner of the window. Now nail the bottom flange at each corner. Repeat this process on one side jamb, but your helper just needs to adjust the unit to plumb with the flat bar, no shims are needed. nail the side jamb at the mid-point, then the top. If you are installing a single hung, you are now locked into position because the fixed upper glass maintains the rigidity of the frame. Nail the opposite flange at the mid point, and your helper is done. Now finish up by nailing the remaining holes. If you are doing sliders or double hungs it's critical to use a level to keep all sides of the frame level, plumb and straight. Finally, use a flange tape to weather seal the flange. The best stuff I found is 4" " Zip System" tape by Huber. It's a thin black rubber tape that sticks better than anything I ever used. This stuff needs to be installed in proper order. The bottom flange gets covered first, then the sides, then the top. Overlaps are then correct, and each piece "shingle laps" over then one below.
My only concern with what you did so far, is why you lacked a nailing surface at the sill of your first window? There is a rough sill of 1-1/2" framing lumber, laying flat in the rough opening of 99.99% of all window openings. If you nailed below this, you may need to shim the window a bit more to raise it up so that the nail slots are hitting the flange. Either this product has oddly large flanges, or maybe it's actually a bit too small for the application? This is an issue I have never encountered before? Good luck, you're doing great so far.