The best, worst and most notable picks, quotes and news from a draft whose dust is just starting to settle.

1. Biggest draft winners

They didn't have high draft picks. They weren't the talks of the event. They weren't involved in any huge trades. Yet the Saints and Cowboys may have emerged as having had the best weekend in Nashville, Tennessee.

Team officials from both conferences say the two NFC teams they think are on a collision course for the conference title-game are the Cowboys and Saints, and the draft helped both, even though neither team had prime draft real estate.

The Cowboys didn't have a first-round pick after they sent it to Oakland for wide receiver Amari Cooper last October. Yet teams and scouts thought defensive lineman Trysten Hill from Central Florida, whom Dallas drafted in Round 2, and Penn State guard Connor McGovern, taken in the third round, were solid choices and could help the team immediately. 

The Saints also didn't have a first-round pick but got a first-round talent in center Erik McCoy from Texas A&M. McCoy has a good chance to start next year and solidify New Orleans' offensive line. Teams also tell me they liked the Saints' fourth-round selection of Florida safety Chauncey Gardner-Johnson, who is expected to be a formidable defender against slot receivers.

"He's one of those players that in the process stood out," coach Sean Payton said of McCoy, according to a team transcript. "I think you see his strength on tape in each game you watch. We really had a high grade on him. He obviously played at a high level of competition, and you see the consistency, and there were just a lot of things to like with the player."

Neither team had far to go to be in the Super Bowl conversation before the draft. The Saints, obviously, were one putrid non-pass-interference call away from getting to the Super Bowl last year.

And while Dallas didn't go far in last season's playoffs, there is, surprisingly, a large contingent of Cowboys believers around the league. Teams respect quarterback Dak Prescott more than many people understand. Throw in running back Ezekiel Elliott, Cooper, a good offensive line and a solid defense, and it's not hard to understand why expectations are high for Dallas.

The draft won't fix everything. The Saints need to get a little better on defense, and Jason Garrett needs to get a lot better at coaching. But this weekend may go a long way toward deciding who the final two teams playing in the NFC will be next January.

2. The good, the best and…the ugly

Best draft: Jaguars. I think two of the best players from this class will be Kentucky pass-rusher Josh Allen and Florida offensive tackle Jawaan Taylor. The Jaguars got both of them.

Good job: Panthers. Florida State pass-rusher Brian Burns has the chance to help instantly make that defense scary.

Something stinks in here: Giants. They took Duke quarterback Daniel Jones at No. 6 overall. That's like taking Ant-Man when the Hulk and Iron Man are still on the board.

3. Watch out, Andy Dalton

There are scouts who believed Ryan Finley was the most starter-ready quarterback in the draft. It's easy to see why.

He's 24 years old. He spent five years playing college football at Boise State and NC State and was viewed at the latter as one of the best team leaders that program ever had. Finley doesn't have a strong arm, but he's accurate (completing 67.4 percent of his passes last season) and extremely athletic. In many ways, he's perfect for today's quick-strike NFL.

That the Bengals chose him in Round 4 shouldn't be considered merely a warning for Andy Dalton. The longtime Cincinnati starter needs to go to red alert. Finley is the kind of player who could step in and replace Dalton this coming season.

This situation should be watched closely.

4. What are the Chiefs waiting for?

Kansas City has released some version of the same bland statement each day since the Tyreek Hill tape—on which he is heard to be threatening his fiancee, Crystal Espinal, who says in the recording Hill physically hit their three-year-old son—was made public.

The Chiefs, however, have done little beyond saying they are disturbed, that they've suspended him from team activities for now and will investigate. They've given no indication of when that investigation will take place or what they need to investigate.

But that won't hold. They need to address this in as transparent and blunt a way as possible before they lose all credibility. And they need to do it soon.

5. Crime and punishment

The idea of punishing teams that draft a troubled player or sign one through free agency is a topic I've written about multiple times, and Pro Football Talk's Mike Florio has rekindled the discussion in light of the latest Hill allegations.

Would it stop the news cycle of off-field violence from NFL players? I think so. If teams thought they could lose multiple high-round picks if a player acts in a violent way, no risky players would be taken, which would either deter players from committing such crimes or deprive those who do of a place in the league.

Taking the picks away would be the easy part. Defining who qualifies as a player who crosses the line is trickier. To me, I'd suggest designating anyone who is convicted or pleads guilty to any domestic violence crime. If there's a second conviction or plea, that team would lose two No. 1 picks.

The problem is, owners would never, ever do this.

The NFL continues to be run with a cold, transactional calculus. So long as the league's popularity remains high and fans overall don't seem to care about players getting in trouble, the league will continue to do very little to deal with the problem.

6. The clock is still ticking for Colin Kaepernick

I've been told for some months now that a team might sign Colin Kaepernick after free agency and the draft. Well, the draft is over, and so is the bulk of free agency. Let's see what happens.

As optimistic as I once was that after Kaepernick settled his collusion case against the NFL that he would be back in the league, that optimism is waning.

7. Meet the Millers

The Carolina Panthers took Alabama linebacker Christian Miller in the fourth round. Smart, hard-working and talented, Miller could easily end up starting next year for the Panthers.

Yet let me tell you for one moment about his father, Corey, who played linebacker for the Giants from 1991 to 1999.

I covered him while working for the New York Times and found him to be not just a tremendous athlete, but also one of the best guys I ever engaged with on the beat. Just a good man and soul who was one of the moral centers of the team.

8. The draft is won in the trenches

According to ESPN Stats & Info, 17 offensive and defensive linemen were taken in the first round. That tied for second-most in the modern history of the draft with Round 1 of 2013.

What does that mean? What do you think that means? It's a passing league, so teams are shoring up their offensive lines to make their passing game better and getting attackers to beat those offensive linemen.

9. Not the next Tom Brady

The Patriots selected Auburn quarterback Jarrett Stidham in the fourth round, leading to the obvious question: Have the Pats found Tom Brady's replacement?

Probably not.

Stidham was asked if he feels any pressure to replace Brady. His response was one of the best quotes from the entire draft. He said, per a team transcript:

"No, I don't think I feel any pressure. [I]t's an awesome opportunity to learn from a guy like Tom. … He's played so much, he's seen everything, he's won a lot—there's just so many different intangibles that I want to soak up from him. I'm sure everybody wants to be as good as Brady one day. I've got to take it one day at a time, and that's what I'm going to do and I'm going to work as absolutely hard as I can to make sure I can do whatever it is to help this organization out."

10. Everyone, and we mean everyone, loves the draft

The first day of the draft Thursday, according to Twitter, generated over three million tweets. Some data from Twitter below on that first day:

The most tweeted-about teams:

1. Giants
2. Raiders
3. Redskins
4. Steelers
5. Cardinals

The most tweeted-about players:

1. Daniel Jones
2. Dwayne Haskins
3. Kyler Murray
4. Devin Bush 
5. Quinnen Williams

The most tweeted moments:

1. New York Giants draft Daniel Jones
2. Pittsburgh Steelers draft Devin Bush
3. Washington Redskins draft Dwayne Haskins
4. Arizona Cardinals draft Kyler Murray
5. Oakland Raiders draft Clelin Ferrell

Mike Freeman covers the NFL for Bleacher Report. Follow him on Twitter: @mikefreemanNFL.