First: congratulations on the new building!
I have to admit that I am not a gutter fan. I have seen way too many issues with them over the years; clogging, leaves and debris removal, rotting the eaves and fascia due to poor installation, leaks...
A geotextile/filter fabric will clog with time. Period. A widely known company swore that their wouldn't, but of course it did,
despite being surrounded with pea gravel. Year one had water flowing out the French drain, year two a dribble, nothing since.
Getting the overall drainage on your site right first is definitely the way to go. When the building is higher than the surroundings, and there are swales to divert flowing water, you are in great shape. The bigger the drop that you can engineer in, the less you have to worry about ponding. Given your site, I would think about how you could add some height to your building base and surrounding area to get the water well away from the flat terrace that you have. I would be thinking about how water from the building isn't going to be a problem for the house and driveway.
Water is the kiss of death for pressure treated posts.
So, a plastic lined trench like
@s219 suggested will get your moisture away from your foundations. If you are worried about other water getting into/under it, make it wider and slope the ground into it to create a reasonable drainage. A plastic lined swale won't clog and will channel water away from your building for a long, long time.
I would make the eaves as large as you can to keep water off of your building, and keep water farther away from the foundation. Your builder should be able to advise you on what wind loads the metal can take in your area.
All the best,
Peter