We did the 6" gutters, and have no trees too close to the house, and the only trees semi close are on the east side (winds tend to be from south to west around here). 4" galvanized downspouts. Smooth 4" PVC drains. So no gutter cleaning problems.
Last house was deep "In The Woods", had "standard" extruded plastic covered aluminum gutters. The 3x4 rectangular down spouts were on them, drains were 4" corrugated plastic. Have had to clean drain lines twice by futzing about with a garden hose. Tried various gutter guards like the ones you posted. Still had to clean the gutters each year, but at least it was on my schedule. So if go this route, pay attention to how hard it is to remove the guards. That house had them attached with aluminum sheet metal screw, so it's a pain. We had gum, pine, oaks and hickory trees, so lots of different sizes of debris.
Extruded 4" rectangular gutter is cheapest, 6" half round metal gutter most expensive. So you are back in familiar territory here reference time, money, and perfection. Young pups trade their lack of money for time and energy, old dogs hopefully can throw extra money at it and save the time and energy (and sometimes they just can't do something anymore).
The old house had the plastic coated aluminum facia on the ends of the roof rafters, no horizontal board. So we could not go back and easily change out the cheaper 4" extruded gutters for the 6" ones. The brackets that hold the big gutters are more extensive and can't go into the end of a rafter. If I were doing it all over, I'd make sure there was a horizontal board at the end of the rafters which the facia was attached to, go with the cheap gutters, and plan to change them out sometime in the future and save for it. This would probably be done in 20-25 years when the house needed a new roof.
I would put in the smooth PVC (3" or 4", depending on how much area the root has) now because you won't want to tear up all your lawn and landscaping down the road. Be sure you have 1/4" drop per foot of run so they self-clean.
Hope this makes sense.
Pete