I agree focusing on the best value player is clearly the way to go. But just so you don't feel like everyone is shooting you down, let me suggest how you might determine which position is most likely to present that value.
You have to know your league's draft history. That's the only time you can start evaluating your draft plan based on position. While you can adjust during the draft, wouldn't it be helpful to know what will happen in the third round before you make your second round pick? That's where position values can be EXTREMELY beneficial.
This is something I started doing about 5 years ago and I can't even tell you how much better I've become at drafting. I started keeping track of how many players at each position (on average) go in each round. This will vary greatly by league, so there is no use in giving you my specific data...plus someone from my league may be watching!
So. Let's say you're picking early in Rd 2. You've got Tom Brady still on the board, and these idiots still haven't drafted Calvin Johnson. The best RB available is #10 on your board. How do you choose? It really doesn't have much to do with how productive these players are...it has to do with how productive the players are that you'll be looking at in Rd 3.
This is where knowledge of your league's patterns really helps. If you know your league is really RB heavy in Rd 2, then selecting your #10 RB might be better than your top QB or WR. But now...let's think two rounds ahead. Because you only get to select one of those positions in Rd 3...the other will have to wait until Rd 4. So maybe if you do take a RB, 10 WRs will be off the board before your round 4 pick. If you take a WR in Rd 3, what QB can you get in Rd 4? If you don't like him, will you go WR again? Are you okay with a 5th Rd QB?
So by evaluating the round by round availability of the players on your draft board, it will help you determine even before the draft has started where you think value can be had. And if this year bucks the trend, you'll recognize it immediately and be able to take advantage of it.
One example...in my league, we have the option of starting a QB in the flex. Because a 2nd QB tends to score a lot more points than a 3rd RB, QB value really skyrockets in my league. But guess what? Nobody else really seems to have caught on to that. So why should I spend a 1st round pick on a QB (even though I have them absolutely valued there) if I don't have to?
Understanding your league can really help shape your preparation of which positions to target in which rounds. You can decide ahead of time if it is better to start the run, or wait until it has begun.