TAY
You and I Know
Phase boots are not particularly good on clock. Moving through units in your cogs to escape is the only real application; the bonus damage is good during a manfight in your cogs, but you'll probably win that with your Q anyway. I usually get tranquils and disassemble them to make mekansm, or just make the mek and keep tranquils. Tranquils are pretty damn good.Phase Boots or Arcane on Clock? I've used both and Phase is nice for setting up Cogs + damage, but Arcane is also good so as to always have mana. What should I get more often than not though?
To fix mana problems you can get soul ring or bottle (though if you aren't getting mek then you shouldn't get soul ring since clock's spells are very cheap. Urn of Shadows is a good choice in that case.) The main issue is getting clock items to be able to stay out on the map indefinitely. With a low cd ult you want to go back to base as little as possible. Arcanes, traquils, soul ring, bottle, and urn all solve this problem in one way or another.
As far as maxing rocket or battery assault goes, I prefer to max the battery assault. Battery assault allows you to more easily get ganks once you hit 6 since it does a ridiculous amount of damage. The rocket's main utility as an offlane clock is allowing you to get some gold when your opponent pulls, which is fantastic, but clockwerk's role is generally such that he starts ganking at level 6 or 7 to kill the opponent's mid or carry, and the battery assault is much better for that. An 80 damage level 1 rocket is completely acceptable for last hitting in lane from afar.
A level 4 battery assault does 75 damage per hit, which is 375 damage even if you only get the 5 hits while your opponent is trapped in the cogs (and you will likely get several more hits than that). IMO the power is better than the utility from rocket, but maxing rocket first isn't bad at all. A lot of people tend to get it first because it's his only nuke (for only 200 damage but w/e); just keep in mind that there are other options.
...but don't max the cogs.
Typically I will go:
cogs
rocket
battery assault
battery assault
battery assault
hookshot
battery assault
rocket
rocket
rocket