The days of protracted rookie holdouts are largely over because of the rookie wage scale the NFL has. It was instituted during in the latest collective bargaining agreement and essentially spells out the contract terms of rookie contracts based on the pick with which a player was drafted.
Over the Cap has a look at the contract each first round pick will get. They are all four year contracts. All are fully guaranteed.
Jets Draft pick Darron Lee is looking at a contract worth $10,221,644 according to Over the Cap. $5,633,924 of that will be paid up front to him as a signing bonus once he puts his name on the contract. It comes out to an annual average of $2,555,411 per year.
First round pick also come with a team option for the fifth year. For players selected outside the top ten picks, such as Lee, the dollar value is the average of the 3rd through the 25th highest salaries at their position.
This is a good example of why you hear it is important to build through the Draft. Lee has the 24th biggest contract in the league at the inside linebacker position. If he becomes a star, the Jets will get great production for around the median price at the position. If he busts, the Jets will be stuck with low production at around the median price.