Painting - Painting Wall and trim

In our hallway, foyer and dining room there is chair railing, and below it molding was used to make 2' by 2' squares on the wall. I believe it was done this way to give the wall the appearance of wainscoting. The chair railing, wall trim, wall and baseboard are all painted the same color. I am planning on repainting this area and was wondering about the correct painting sequence. First, I was thinking of painting the chair railing, the molding, the area inside of the square molding, the wall, then the baseboard. Is this in the corret sequence? Also, how do I paint around the square molding without leaving brush strokes that look like a box around the 2' by 2' molding?

Your sequence is correct in my book.

After cutting around the boxes/trim, use a roller and do a 'french cut', meaning roll sideways right up on the cut, close to trim as possible.

prowallguy - what type of roller do you suggest? I was thinking a high end four inch foam roller.

Thanks

4" for sure, I prefer the Wooster Jumbo-Koter. (http://www.woosterbrush.com/products.asp?id=195) Scroll down and check out the Super Fab or 50/50 covers for it.

prowallguy - the two examples you gave state the following:

JUMBO-KOTER® SUPER/FAB®
• Offers exceptional capacity with all flat or satin paints, stains, and sealers

JUMBO-KOTER® 50/50™
• Golden yellow fabric blend of 50% lambswool and 50% polyester for 100% performance in all flat or satin paints, stains, and sealers

I am using a semi-gloss, will that be a problem?

Also, thanks so much. You have been a great help.

Semi-gloss will work with both too.