I'm a fantasy draft nut and probably put way too much thought into it, but here is what I do:
1st two picks on big mashers if you want an offensive team. Or first 2 picks on aces if you want a pitching team. I usually like to use my first two picks on all around players; SS/CF/3B/C that can hit, run, steal, play D, durable.
Round it out with picks 3-4. Take 2 pitchers if you got 2 hitters or vice versa. I'll usually go value with pick 5.
Like the other guy mentioned, I like to take stud relievers with 6 & 7, before the CPU takes a run on them. During that run, you're free to pick whoever you want offensively. Since the CPU literally picks all RPs for 60+ straight picks.
Then, I just start filling holes with best available. Like I mentioned in another post, try to avoid scrolling down to cherry pick the A rated stud 18-20 year old prospects. If you want, you can draft like 30 of them and have a dynasty better than the Yankees
There is so many ways to go. I think you will find the most fun in running a few dozen mock drafts, to see where your dream first pick lands, and your 2nd & 3rd round dream steal picks land. (Cheesy I know!)