I'm not going to tell you how many players you should scout per week. I will tell you, however, how the draft works, so that you can decide for yourself.
There are 48 players in the draft, which comes out to three rounds for the 16 teams in your league. Each player can be scouted twice. The first time you scout a player, you discover his "star rating", which is a rating from one to five of, generally, how good the player will be. The second time you scout a player, you will receive a more specific "grade ranking" (i.e., from A+ to F), along with the player's best attribute, and how high it is. You cannot choose the players you scout; they will be picked randomly.
A couple weeks before the draft, you pick the order in which you want to draft prospects, based on the information that you've gleaned from scouting. When the draft is run, the highest available player on this list will be given to you in each round.
It's up to you to decide how much emphasis you want to put on scouting. It's definitely a balance between keeping your weekly budget afloat and trying to figure out who is the best player available.