I prefer games that are just starting out or have not started yet. I like to be in games from the very beginning in order to completely understand everything that's happening and has happened.
Otherwise, games with a small number of muns is something I can handle. In short, I prefer games that aren't vastly populated or that have been around for ages.
If a character I'm applying for has been played in the past, I'd like to know the back story of said character before I spend my time on an application to make sure the old character and mine are comparable.
Believability is one of the most important things I look for in a game. I need a balanced environment. I need the Order, the Death Eaters, and the Ministry to all be active and doing things even if characters aren't played from a certain faction. It isn't believable to me that the Death Eaters, for example, are running around meeting "law abiding" characters in game and having said "law abiding" characters talk about it in their journals without the Ministry realizing, "hey, maybe we should investigate this supposed "law abiding" citizen and see what's up!" Understand what I mean?
Plot: I like my games to stick to the plot outlined in the game's userinfo. If there's a war on the horizon and the Wizarding World is trembling in fear and anticipation I want there to actually be a war and the general populous to be concerned about it! I don't mind if games are strictly smut and romance, just be up front if that's what your game's about. Sometimes I join those too!
Slash acceptable! Even if the character I play is straight, I dislike games that are strict on this rule.
A certain amount of freedom is appreciated. Games that are religiously canon are not for me.