dc is a little different for me but you can look up characters in the marvel.wiki dc.wiki sites just to get a gist of what's going on with a synopsis and character profiles. they give a decent starting point if you do a little research and they also tell when the stories start issue wise
My advice is - don't get lost in continuity. Don't get obsessed about knowing everything. Don't go "I will start with issue #100, and work my way up to #300". You'll get bored, since there's much shit in between good stories.
If you like a character, google their best stories, and go from there. The same with teams. In fact - I even recommend starting with teams, since you'll just branch off into the individual members' arcs afterwards. They don't even have to be in continuity. In time, you will see what type of story you like, discover new characters, and also whose writer's comics you enjoy, so you will also start reading up on them.