To the bottom of the elite player talent pool (whatever it may be) and with the exception of QBs (and sometimes but not often other positions), I believe every team in the NFL honestly tries to take the best available football player. An article written in the mid 70s about a series of interviews with Brandt and Schramm explained the mathematics of drafting, and the necessity of building your franchise with the best football players you can draft regardless of position (in most cases).
I do believe the last decade of drafts has followed this thinking for the most part. It gets complicated several dozen ways, but primarily is the fact that 32 teams see the elite talent 32 different ways. A year ago, the Niners Personnel Director (Scott McCloughan??) claimed they tagged 18 elite players in the draft, BUT they got one with the 22nd pick, AND "another" was still available.
Balancing needs and talent is generally far more important after the elite prospects are gone and for as long as the "obvious NFL talent" is available. Many things factor into this too, and I'm beginning to believe "depth per position" supply and demand thinking is very important.
Once the "obvious NFL talent" is gone, which never happened last year, that's when measureables become very important if you want to be drafted. Parcells has a quote on this. Paraphrasing, "With those sixth and seventh round guys, you need to know that he has the physical strength and speed to hold up. I can try to coach him, but I can't do much about his genetics."
Then there's the team preferences and tendencies too, but they aren't static and can change. No one saw the Pats going Maroney Jackson. It seemed so out of character, but made so much sense.
Good call. I cannot remember the phrasing or exact wording but his (Brandt's) feeling in that article was that if a team constantly takes guys they need, meaning players meeting a positional need, versus guys with talent, which would be difference makers and impact players, that team kicks their a** kicked on Sundays more often than not. He then went on to explain that the top few picks are for impact players especially Round 1 and to a lesser degree Rounds 2-3. He summarized by saying you take guys that win you games early on in the draft and guys that help you win later in the draft.
I think most teams follow that type of formula suggested by Brandt, while placing a different level of importance and or emphasis upon things like...
Signability...How easy will it be to sign the draftee and who is his agent?
Short and long-term economics of signing the draftee...Can he be easily resigned after the first contract duration?
Does the draftee fit into the current offensive or defensive system or not?
What is the draftee's character?
What are his measurables and physical abilities?
Will signing this draftee be contrary to the franchise's historical operating rhythm? For example, will the draftee's contract be more than the team has spent in the past; will that contract cripple future moves due to the salary cap or will the team be held hostage by the compensation package, etc.
What type of bottom dollar impact could the draftee have on sales?
Will he help us win games now, tomorrow or next year?
What combination of ROI...money v. player v. return...rests with this draftee?
Those are in no particular order but taking a player is at times equal parts sales, operations, scouting and coaching.
This is why you see a few

picks over the course of Round 1 especially picks 1-15. There are always 1, 2, 3 or 4 picks that leave the general public feeling odd, uncomfortable, giggling or in a state of shock. The reason being is that the value table and proposition chart/formula used by each team is just a little different.
It is sort of like that idea that one man's art is another man's pornography. It varies a great deal and, as we have come to know, an imperfect process. Some teams, though, work the process versus getting worked by the process more often than not.