You become James Hetfield.

There is no definite 'slow' speed or 'fast' speed for you to follow, for example, lets assume that a song you want to learn is played at 200bpm, so you drop it to a level that you can play all notes cleanly without any mistakes whatsoever. Once you're able to do that for a few runs, bring it up another 5 or 10bpm and continue practicing. You could do speed bursts occasionally as well. Plus for downstrokes, try to minimize your wrist movements and keep your arms as relaxed as possible. If you're playing standing up, putting the strap low so your arm extends helps to a certain degree (I believe this is personal preference, but there's probably a reason why Hetfield has his guitar hung so low).

Hope that helps!