I like something "special" or "unique" about a dynasty as long as it doesn't get too freaked out. Random debut is too freaked out in my view. Star Trek taught us not to play with time, unless the plot absolutely requires it to conclude an episode. If Nolan Ryan had been meant to pitch to Babe Ruth, Ryan would've been born in time.
It really is a matter of quite a few different factors that have to come together to make a dynasty interesting to me, like an interesting setting, a guy's ability to write in an interesting and comprehensive way, and I like a combo of text and graphics. A picture tells more than a thousand words, so it's probably best to post the main stats of your roster from time to time instead of elaborating the home run race in three paragraphs.
I'm that Raccoons guy (obviously) that does nothing fancy and I find that over the 18 months that I have written that dynasty, I have changed my style a ton (and I hope improved it towards being a lot more comprehensive, the first few pages were a mess

).
I'm still striving for that perfect balance between amount of text and actual content. I tend to get lost in situations where my team is leading by five runs in the eighth inning of a game in mid-May and proced at-bat by at-bat there - completely unnecessary at times. If you look at Orcin's dynasty, he does a wonderful job of posting a week's results, top and bottom performers, two or three updates here and there. I can't keep myself so short, my fingers want to type!