I usually watch anime based on personal recommendations - and I've got 51 titles on my "Plan to Watch" list, so...I'll be busy for quite some time
But the anime I tend to gravitate towards are ones that break the mold somehow. I became fed up with the shoujo and shounen tropes early on, and sought out animes that did more interesting things with their stories and were harder to define in neat genres. I like shows that have very strong plots and relationships - though I've discovered that I'll put up with lackluster plots and annoying tropes like wildly impossible fights with people hovering in the air for five minutes while yelling out their attacks...
if the characters and their relationships are compelling. Fantasy and supernatural elements are always a plus, but not necessary - I'm currently reading Liar Game, which has nothing supernatural and is just about human nature. And it's
fascinating. I also find myself gravitating more towards realistic character designs rather than the more stylized ones.
I don't think I've ever picked a show for one of these reasons, but after getting a recommendation for a show, my interest is immediately piqued if it's done by Bones. At the very least, I'll know that their animation will be beautiful to look at. I also like to check out the voice actors and see if I recognize any (though of course, if I'm watching the dub it's usually FUNimation and I'm familiar with most of their main voices
) As for length, I like the normal length of 26 episodes. Few stories, if you ask me, are strong enough to hold up for 100+ episodes; I have yet to put up with one for that long. It's usually an indication of the creators not knowing how to end the story or milking its success for more than it's worth.
Unless I get a personal recommendation from someone who knows exactly what I like in a story, I'll actually watch a random episode to see if it looks promising or not. I get weird looks whenever I mention this, but I've found it to be extremely helpful. I pick an episode roughly three-fourths of the way through the show, then watch the subbed version and cover up the subtitles. I don't know enough Japanese to understand exactly what's going on, but I can get a really good indication of the tone and nature of the show. Since it's so far into the story, I have no idea what the significance of anything is, and since I stick it on the end of my very long list and probably won't get to it for years, I forget most of what I've seen anyway by the time I actually watch the anime. This method hasn't steered me wrong yet.