If your gates are wooden, they will sag1. Even if your gates are metal, they may sag. I would recommend 6x6 if you can manage to find a friend, but I would also recommend you sink them 3ft into the ground if they're 6ft tall above ground.
To deal with sagging, use metal cables that can be shortened/tightened, either with clamps at the end where you can periodically unclamp and tighten the metal cables, or with a metal cable turnbuckle/tension hook in the middle somewhere that you can tighten without having to detach first.
There are already other excellent posts on this site about how to hang a fence post to prevent sagging based on the material used.
1: If you don't believe me, last year I built a custom fence in Georgia using 1x4s for the panels (with hog wire sandwiched between two 1x4s) and 4x4 posts; 4ft tall fence with 2ft buried in concrete footings. The gate panels are 4ft wide. Alone, the gate panels are maybe 5 pounds... which is very light for a gate. Less than 1 year later and the gates have started sagging; not much, maybe 1/16th out of level, but it's noticeable when you look at it up close. I also cut one gate to be a pretty snug fit, and it has since started scraping against the latching post a bit, which again indicates sagging over time.
(For reference, I used this hinge hardware: 8 in. Black Heavy-Duty Decorative Strap Hinges by Everbilt)