I am no expert so take the following with a grain of salt.
I did find this link to a stratics forum post that i found interesting:
http://boards.stratics.com/php-bin/uo/showflat.php?Cat=3&Number=6711020&page=0&view=collapsed&sb=5&o=&fpart=1
I believe all the timers on the keys are the same, which I believe is 6 hours from the time they spawn.
This is except for Lady Mel, where have to do a quest that never expires so can do it days or weeks before you turn in the quest for the boss keys.
Easiest, depending on char most likely. I am building a char to solo getting Travesty keys, as for me that appears like maybe the easiest. I am tweaking my stealther to get the orange key, but the other 2 are easy for most chars, I use a pally to disarm, but stealth mage casting EV's is probably better.
Lady Mel, is next on my list of easiest, just have to kill 12 insane dryads and 1 named stone harpy (haven't done this with my pally yet but hoping with right equipment to walk through it, worried about the changlings in the area though)
I hear Dreadhorn is the next easiest, but my experience for gathering keys ends after the first two listed. I suspect Shimmering/Proxy/Bedlam are the 3 hardest because of all the heavy spawn and named monsters to deal with.
If you want to have keys for a peerless, I would suggest keeping a Lady Mel quest completed on a char as a last resort since it won't expire. Then if you can get good at getting Orange Key for Travesty, then should be able to farm multiple sets of Trav, since the blue and yellow are pretty easy to get (I have found several laying on the ground because people gave up trying to get the orange).
If I can get a char that can easily do the Lady Mel quest I will try and keep a char with quest completed on hand. Oh also, another thing nice about the Lady Mel quest is if go in a group multiple people can complete the quest. I went with a group of 3 people, we all did the quest, which is easy with 3 people, then we did 3 Lady Mels.
If there is anything left after my 2 cents clears the bank, put it towards my account.
I have never done a shimmering peerless so don't know how they are.