However, certain things do become issues once your dwarf population scales past 15 or so. Checking dwarf occupations manually (e.g., to make sure that there is at least one dwarf who is currently assigned the furnace operator occupation) becomes a pain, so I'd suggest using Dwarf Therapist [0] to manage that. It also lets you quickly check other things, such as whether any dwarves are feeling particularly sad.
Also, I encourage people new to the game to check out some of the stories that the community has generated throughout DF's existence. The game's ability to generate interesting scenarios that lead to good stories to tell your friends is perhaps the most interesting part of the game. Boatmurdered [1] is a classic. Roomcarnage [2] is currently in the process of being told and is quite good.
[0]: https://github.com/splintermind/Dwarf-Therapist
[1]: http://lparchive.org/Dwarf-Fortress-Boatmurdered/
[2]: http://www.bay12forums.com/smf/index.php?topic=139393.0