I'm an AD Assassin player, so note that my post is largely from that perspective.
In my opinion, you should never spam your abilities. Any good mid laner, especially one with even the least bit of competency to dodge your spells, will abuse the hell out of your Cooldowns by timing their hard engage while all of your important abilities are still recharging. Especially against champions with high kill potential, a misused ability can easily lead to your immediate death, or at least the worst trade possible for yourself.
For example, I was able to turn around a losing lane as Talon vs Ziggs when I noticed that he kept trying to use his Satchel Charge to attack me. The next time I saw him use his Satchel Charge, I immediately used Cutthroat to both negate his Charge and get me on top of him, wailed away, and got myself a kill on him despite being two kills behind. From that point on, I snowballed hard because he insisted on spamming his abilities instead of saving them specifically for when I jumped on him.
Depending on how well you CS with auto attacks, you really shouldn't need to use your abilities, well, at all. Again, AD Assassin player here, last hitting is phenomenally easier for me than it is for an AP Champion if you ignore the part where I can get harassed, but my point still stands. Mana shouldn't be a concern unless you are doing something terribly dumb.
During Teamfights, ranged mages are basically a combination of Marksmen and Cleanup Crew. Your job is to stay as far away from the fight as possible while still remaining in range to use your own abilities. Personally, I suggest itemizing for tank busting if necessary because the squishiest targets are either too far away or stand behind a wall of meat shields. For Ziggs specifically, I'd save your ultimate until the fight is coming to a close and/or the enemy team groups up heavily. The latter is obvious, and the former can be used to pick off any survivors that try to run away.
Technically speaking, Ziggs' main strength is his wave clear, therefore you really only need enough AP that you can clear entire waves with only a single rotation of your abilities, or can blow up monster waves with only your Ultimate alone. If you feel that you are getting nuked too easily late game, I don't see what's wrong with itemizing somewhat tanky.