Optimal Perks

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Attack
Has a 2% chance for degradable items to not degrade. This only applies to degradables with a charge-based system, including augmented degrade-to-dust (normal augmentable items with drain rates are not affected – see Invention perk below). Since this works on expensive items like augmented T90 armor and hydrix, this can be extremely good to shave off costs across the board.
 

Defence
Acts like a portent of life. Self-explanatory, if you do not have 99 Divination this frees up your pocket slot for something else like a scrimshaw. Even with 99 Divination, this allows you to carry an additional item in your inventory, allowing for more supplies.

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Invention
Has a 2% drain reduction. Basically the second half of the Attack perk, but works on augmented items. Again can be very good to reduce costs in combat.

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Strength
Adds three additional hits to Dismember. This is basically a 60% buff to Dismember, one of Melee’s best abilities. This perk makes Dismember at least not a waste to use under Berserk, whereas without the perk Dismember is the worst ability to use under Berserk. Paired with a Lunging 3 switch, Dismember becomes one of the single best basics in the game, beating Corruption abilities in single-target DPS and coming very close to a walked Fragmentation Shot/Combust. Even without Lunging 3, it comes extremely close to Corruption (only 8% worse), so Melee pretty much gets another very strong basic to use. Definitely consider using this perk if Meleeing.

Any of the above are the absolute best perks to have on your max/completionist cape. Pick and use what you’d probably get the most use out of, then work your way from there.

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Situational Perks

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Constitution
Doubles regeneration (except for banks). In general this is useless because regeneration is turned off during combat, but with Fortitude on regeneration is reenabled. This perk doubles the amount you get from having Fortitude on, but due to the lack of uses for Fortitude in general this is extremely limited in use. That said, if you get good use out of Fortitude like at 1000%+ Telos or Raids basing, this perk can see a bit of use as it can actually influence something combat-related, unlike Attack/Defence/Invention, but if you don’t use Fortitude for direct combat, skip this perk completely.

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Divination

Has a roughly 1/30 chance to save Divination materials when creating Divination products (excluding divine charges). Very good when making portents of life/item protection, converting cursed energy to incandescent energy, or doing anything else production-related with Divination. Not worth putting on a max/completionist cape though, just keep it in bank.

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Dungeoneering

Teleports you to any resource dungeon. Extremely useful for stuff like teleporting to celestial dragons, Kal’gerion demons, and more, but limited use aside from that. Not worth putting on a max/completionist cape though, just keep it in bank.

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Magic

Provides free spellbook swapping near a bank. Pretty self-explanatory, extremely useful when gearing up for a different boss for absolutely no cost. Not worth putting on a max/completionist cape though, just keep it in bank.

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Slayer

Provides free teleports to every Slayer master in the game. Useful if buying enchanted gems to later make into slayer rings for disassembling or simply getting a different task. Not worth putting on a max/completionist cape though, just keep it in bank.