$60m theme leagues and progressive leagues are the most realistic. $60m leagues will give you stats that mirror their RL stats the closest and progressives will also tend to give you leagues that mirror RL stats closely, while also featuring just 1 instance of a player in a league. Depending on the theme rules for a $60m league, there may be some leagues that will allow multiple instances of a player per team (clones), but many do not allow clones. In fact, there is at least one $60m league in the classifieds that may be of interest to you: No clones, and the theme rules for IP per pitcher will make it such that pretty much every team will be running a 5 or 6 man rotation unless they get creative on their managerial settings.
As for progressives, there's alot to choose from and there is an entire classified forum just for progressive leagues.
I bumped the $60m league ad towards the top of the theme classifieds for you and you should feel free to peruse the progressive classifieds to see if there is anything there that interests you as well.