POTD as in Palace of the Dead? Dude just queue up and faceroll through it. Why would you even try to solo something intended for four players
Can you queue up for it? I didn't think it was on the Duty Finder.
It's not in the Duty Finder. You have to talk to an NPC in Quarrymill get in the POTD queue, but once you're in it, it works the same way as any other queue does.
On POTD, Floors 1-50 are crazy easy, you just have to remember how to play your classes at really low levels. And you get an ilvl 235 weapon out of it. It probably takes 3-4 runs of floors 1-50 to get it, less if you're doing Floors 50-100. It's a great way to relearn how to play classes if you haven't played them in a while. And if you want to sink some more time into it, you can also get ilvl 255 weapons as well...
Anima quests are all about using classes other then the one you're getting the weapon for to get drops. And about using the Roulettes as that's a great source of tomestones. It's also about figuring out what stages of the weapon are easy to get and what aren't.
IE: while getting my SMN anima weapon I leveled up Astro for fate drops/ather oils/poetics tombstones. The grind up to Hyperconductive is really easy now, so I got that for AST and am in the process for getting it for DRK. The Umbrite grind to get the weapon after that is insane though, so I'm holding off on that until it gets nerfed.
Haven't done Relic quests, but I have several classes at lvl 50 and I want to level them up to clear out my equip inventory. So I'm thinking about doing the relic quests if simply for an excuse to do some FATE grinding. It'll also eliminate a step in the Anima quest, so that's good too.
Quick and Dirty guide to getting your ilvl up
Gearing gets way easier for the other classes once you have one class leveled up. Then you can start collecting equips for other classes so that when they get to lvl 60 they already have decent level gear. Good equips to prioritize (aside from the class you main) are Tank, Healer, and Long Range DPS gear as those will gear up multiple classes. Meele DPS gear only gears up one class, so that takes up a lot of space.
On weapon equips: When you get to lvl 50, you'll probably want to run Shiva Extreme (unsynced) to get Diamond weapons. They're better then the weapons for sale in Ishgaurd and Shiva is a really easy Extreme to beat when unsynced (no anti-DPS mechanics). They also won't be outclassed until you get to the lvl 55 dungeon. The lvl 55 weapons are really good to get too as they outclass the lvl 60 weapons for sale in Idllyshire. Around lvl 55 is when you should start doing POTD so that when you get to lvl 60 you've got a Padajali/Kinna weapon waiting for you already.
On armor equips: If you're not doing Anima, feel free to get Ironworks gear at lvl 50. If you run a lot of World of Darkness, then those equips work just as well. It'll save you a bunch of gil. Get gear from the lvl 55 dungeon as that's an upgrade to both those sets. If you you're leveling your first class to lvl 60, then you're in for a bit of an equip grind. If you're not doing Anima, Tombstones will help out a ton. The main thing you're aiming for is Expert Roulette as the ilvl gear that drops from that is good enough to get you into raiding content. You can also get that gear for your other classes so you only have to do a major gear grind once.
On Roulettes: As annoying as tracking down all the dungeons needed for the Roulettes can be, doing so is a good idea if you want your equip grind to be as painless as possible. Roulettes are one of the biggest sources of Tombstones in the game and Tombstone gear is a higher ilvl then all the equips available in dungeons until it's phased out. Getting the Roulettes unlocked means you have to run less dungeons for the same amount of Tombstones so you can get gear faster and more reliably.
For me, half the fun of playing games is playing them as efficiently as possible. In most MMOs that equates to grinding efficiently. Fortunately, FFXIV has a lot of ways to do that...