Normally, it is good practice to avoid pools until after the PC has completed the arena. Given the other possible risks from pools (dooming, aging, teleportitis, to name a few), it isn't usually worth the risk so early unless there's some really compelling reason to do so. Being unable to (easily) complete the arena deprives the PC of tactics, some nice items, and Big Punch--quite a respectable early game weapon if the PC hasn't been too lucky up to this point. The arena also gives the PC the backstabbing skill, which, it is worth mentioning, is pretty good if you happen to be invisible.
That said, invisibility is a fantastic intrinsic for almost any class, since, by and large, you can always pick where and when you want to fight since few early game monsters can see invisible; cats become essentially a non-issue once you have it; your damage increases dramatically in combination with the backstabbing skill; many annoying early-game areas (SMC, animated forest/DH, hostile big room, etc.) can be crossed much more easily than would be possible otherwise; many dangerous early-game monsters can be avoided entirely (eg. vortices). Of course, if you have spells, many of these effects can be reproduced in principle, but not as conveniently.
Hoping to win with every class, doomed. Archer, Barbarian, Bard, Beastfighter, Druid, Elementalist, Farmer, Fighter, Monk, and ULE Priest down.