A few notes.
Take two dwarfs, preferably ones that come with some combat skills, and put them in a squad. Equip them with whatever weapons and armor I can produce or buy.
If you equip both of them with the same weapon then they will learn a fair bit faster. In a worst case scenario you can give them both training weapons made of wood until they are able to get real ones.
Danger rooms are much faster, but I find them too much of an exploit and never use them.
An easy way to nerf your danger rooms so they are a much more realistic training mechanism is to attach them to a pressure plate in a high traffic area instead of a lever. Danger rooms set up in this way can only have a maximum rate about 2.2x slower then a normal danger room, and as your population increases they will slow down even more. As such they are a nice way to start up a military but will actually become slower then normal training methods once you have skilled dwarves and a large fortress.
If you don't mind changing your starting build a little bit there is a very easy way to set up a very powerful military very quickly.
1)Give 5 of your starting 7 dwarves 5 points in a military skill (such as armor user, dodger, fighter, or a weapon skill) and 5 points in the "teacher" skill.
2)As soon as you can put the 5 dwarves in a single squad and let them train with each other. They should very quickly learn since demonstrations are one of the fastest teaching methods out there short of a danger room (assuming that there is a high skill difference in the taught skill between the teacher and student, and the teaching dwarf has a high "teacher" skill).
3)Once the dwarves have reached the point where they are all skilled in all 5 skills then you can break each of them apart into 5 different groups (or less if you don't have that many dwarves). Fill each group up with new recruits which should begin to gain skills extremely quickly.
4)Once the recruits near their teacher's skill level then break them off into the normal squads of 2-4 to encourage sparring.
In this way you can easily set up a very skilled military almost as fast as if you use a danger room without actually needing to "cheat" as some deem it.