Ok, there is a trick to accomplishing what you want. When I did a lot of these (former general contractor) I could do a window in about 15 min. This is not rocket science, and don't try to over think it......
Cut your header piece (top of window) first and make it a bit snug. If you have to, scribe the piece to fit perfectly into the space, but put the cut side to the window, a little caulk will fill small gaps and paint well. You want to have to gently tap it into place, but not have to bang it! use a square and shims to get it square to the window casing as possible then finish nail into place, leave the shims! Do the same with the side pieces (vertical sides). Once all is fitted and you are happy, scribe and snap off shims and case the outside leaving 0-1/4 inch reveal, this is a personal call. From the pictures you posted, you have a wooden stool (many call this the sill, but the finished piece is called a stool). This may require a creative bit of thinking to blend the trim, or you may wish to replace it and leave the "wings" a bit longer to accommodate the new case frame. Feel free to PM me if you need any more help.