They're all rng based aside from Red, Ulduar and Violet. Violet is easiest as it's a lot of work spread across the whole year, but that doesn't fulfil your specifications unless you've been keeping up with the holiday achievements. It was the first one I got I think (the Halloween after it's theoretical earliest possible acquisition, due to the Sinister Squashling).
Green is by far the least effort beyond the initial rep grind. Get the Wolvar stuff first though, (if you want their stuff) as they all have decent drop rates, whereas the Green may never drop (in theory). I got mine in about 4 months (you can try once per week). YMMV.
Blue is probably the quickest as you can try once per day.
The thing is though, you can do all of these at the same time as they require small amounts of time commitment, and keeping an eye out for Ulduar runs.
TLPD is the one you're least likely to get easily as it requires the rarer version of a rare spawn, in a heavily camped crz. Time lost indeed.
And Red might be possible, might be impossible depending on mechanics of certain fights in Wrath 5 mans (though most can be brute-forced). Those aren't dangerous, but fulfilling the kill requirements might be tricky.