Floors first. It limits the flooring installer too much with the odd angles of the house to make him try to hit it right on. The baseboard is there to help hide boogers. Shoe molding is there to hide bigger boogers.
Floors 1st guy - Easier cause floor doesn't have to be cut flush to wall
Baseboards 1st guy - This allows floors to expand and contract and without seeing any gaps against baseboard, looks cleaner, easier to repair if needed. Also if you put floors first you will see gaps under baseboard if subfloor is uneven and as the floor expands and contracts.
Baseboards will lay in a straight line. They will not bend with aberrations in the floor should there be any. You will have gaps and it will look pooky at best. The baseboard guy will be guessing at the proper height. Flooring should be installed first, then attempt to lay baseboard as close to flooring as possible to alleviate gaps. Should gaps be a problem, then consider shoe molding, not quarter round. Shoe molding bends in both directions for a cleaner fit.
Floors first. Manufacturer of flooring will specify that there should be a 1/2" to 3/4" expansion gap parallel to the flooring.....expansion gap at the ends of rows is negligible. The gap can be created by allowing the flooring to run under the baseboards or shoe molding, if used. If baseboards go in first installer would have to leave an expansion gap between the flooring and baseboard which would not look good. If the flooring is installed tight to the base board you would be asking for trouble and not following the flooring manufacturer's installation instructions. I would be leery of the baseboards first guy. I'd be leery of the other guy's answer about having to cut flush to baseboard....shouldn't be cut flush anyway.....need the expansion gap.
Just to be proactive....the flooring should be acclimated to the proper moisture content before installation. This can be tricky in new construction if everybody is trying to beat the clock to get their work done. Based on your location I assume the house is in the Boston area and besides the summer high humidity new construction will have high humidity from the trades doing drywall, etc.
The problem with installing floors that haven't been acclimated in the summer is that once the humidity goes down the floor boards will shrink and there will be gaps between the boards.
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