NOTICE! I have discovered that I was partially wrong. There is a difference between weapons. While every weapon of a certain type (ie, every rod) can obtain the same maximum stat value after grinding and extending, not all weapons have the same Potential.
This is something I didn't cover very well, but have managed to piece together the information now.
Every weapon (generally 6+ stars) has a potential. To unlock it, you must grind it up to +10, then use Photon Spheres to reset it to +0 but give it a unique ability. These vary from things like +Fire damage percentage to +guard stance effectiveness. Every weapon that has a potential only has ONE potential. Since I'm a career force, the list of rods here:
http://pso2.cirnopedia.info/weapon_11.php#navshows the "abilities" of weapons near the right. The ones that are yellow and red with a star-ish shape, are potentials. The weapon DOES NOT drop with that potential, but rather that's the potential that can be unlocked. For instance on the list, Red Processor is the first rod that has a potential, which is Circuit Breakout (+T-ATK when using Photon Flare, a Force skill). This means that however you obtain the rod, when you +10 it and unlock the potential, it will always unlock Circuit Breakout.
So, looking at the list, there's a few weapons I would want. Weddle Park has +Dark Damage, which is great since I adore Na Megid's massive damage bomb, but there's also Vibras Rod and Chrome Evol that give +Damage vs Darkers (Weddle gives a higher damage bonus, but Vibras is a lower rarity so easier to get). Then there's a few that give PP consumption benefit, or PP recovery rate, both of which are very useful.
So find a Potential you like, mouse-over them on the list to get a tooltip, and search down that weapon to work on upgrading. You can usually buy one on market cheaply, and you put in the effort to upgrade them. Finding a highly upgraded weapon is more expensive, but you can find even 11star weapons with poor starting abilities somewhat easily.
Also worth noting, for those maxing out damage, 6 abilities. Force as an example, Technique, Ability, Returner, Technique Boost (which is a premium ability), Flict Magia, and a boss soul, can get +160 T-ATK, along with a spattering of PP and HP. You could theoretically get this on 4 items, your weapon and all 3 armor items, for a total of a thoroughly expensive +640 T-ATK (which is about 1/2 of the value of a maxed weapon, so that's basically having your weapon's power by 1.5x).
The game really allows options for maximizing, but the prospect of actually grinding everything up is an enormous feat. 12 Photon Spheres, ~100 grinders, and probably about 1,500 weapons with desired abilities to reduce and refine, and you might get your maxed out weapon. Then do that 3 more times for your armor options.