You get equipment seeds mostly for free anyway, so there's little reason not to use them, really. Wether you use the forge to upgrade the seeds or not depends on how badly you need equipment. Upgrade if you need quality, don't if you need quantity. Either way, event stuff and whale airship stuff is better. You can get a bunch of them from the permanently reissued events too.

When it comes to leveling them though, it's much cheaper to level them a lot all at once, rather than level them one bit at a time. You can max out a silver event item with 4 gold upgrade materials and some junk, in one go. It's the cheapest option by far, since it bases the gold cost per material on the items current level. Doing it in stages can quit literally cost you 100 times as much money. Leveling characters works the same way.

Forging upgrade materials into higher tier materials is worth it only to save on cost. You can only apply 10 materials at once, after all, and the more you use at once, the better. The overall item exp you get from it diminishes a bit though (3 silvers gives slightly more exp than one gold, but only a little bit). It's not worth it to craft neutral materials (the anvil icon), since they lack the item-specific bonus. Earring material gives more exp to earrings than to other items, for example. A neutral material gives (i think) the same exp to a bracelet as an earring material would give to a bracelet.