Doors and latches

OK, got my doors hung, used counter top edging around the door opening and T molding around the edges of the doors. The interior of the doors lacks about 1/4" from flushing up with the interior walls (due to the trim). How do you guys compensate for this? Should I just notch out part of the opening so that the latch bolt will catch?
I bought my latches and handles from Austin Hdw. The handles have a shoulder on them, underneath the mounting plate approx. 7/8" diameter. When drilling the hole in the door to insert the square handle should I drill a hole for the shaft, about 3/8" diam. and then drill the 7/8" diameter hole to countersink the handles shoulder or, do you guys just drill a 7/8" hole all the way through the door?
I bought my latches and handles from Austin Hdw. The handles have a shoulder on them, underneath the mounting plate approx. 7/8" diameter. When drilling the hole in the door to insert the square handle should I drill a hole for the shaft, about 3/8" diam. and then drill the 7/8" diameter hole to countersink the handles shoulder or, do you guys just drill a 7/8" hole all the way through the door?