So is farming keys and doing the machine the best way to spend your time in-game?
That's what I do basically. The infernal machines are the "end game" currently, although if you lucked out and already got a really well-rolled ring, it's less of an imperative. Basically get 5 stacks in acts 1, 2, 3, kill keywarden, and hope to get not only keys but also some legendary drops while you're at it.
Now, the other way to go is just go with experience and focus on leveling your Paragon levels. Getting keys is not the efficient way for this, because it's not the best exp/hour. If you want to just focus on Paragon levelling, then you want to do runs, like act 3, or the assassin's place in act 2.
Personally I play casually, maybe an hour or 2 if I happen to play, and I find Paragon leveling too boring and tedious. Not that key farming doesn't get boring either, but it at least varies up the scenery a bit more. Additionally, I don't think I would focus on key farming unless you could do it on MP4 or above....remember it's about 10% chance of a key dropping per MP level, so at MP1 it's only 10% chance....I believe MP0 is 1%. So you would be better served to level Paragon levels, farm for gold/better gear, and then do key farming on MP4+. This is solo of course....if you can group you can tag along with better geared people and do whatever MP level you guys are capable of. Currently I farm keys at MP5-6 solo, my buddies and I just farm keys when we aren't all online together, and then when we are online together we will kill the uber bosses at MP8.
Also to answer your wizard question, yes, imo blizzard/hydra is obsolete, because you want to maximize your killtime, so archon and CM builds are more efficient. Unless you were uber geared, I don't think you would survive the higher MP levels, and if you could somehow kill in MP5+ with a blizz/hydra build, then definitely you could kill faster with an archon or CM build.