They will want to visit your school when you gain enough interest. Sometimes they are ready as soon as week one sometimes it takes a little longer. You can have as many recruits in for a visit on a set week as you want. So you can put them all on one week and hope you don't mess up ie take a loss. Or spread them out over your rival games or big games. I like to get them in early if possible but it doesn't always work out that way. I don't really like having recruits in for user vs user games in my OD's because you never know how those will go.
If you really want a top player or just someone you rate very highly I would say offer him the very first week. You will be able to go back as your season runs and as your board gets a little empty and see who hasn't got a offer yet and you can attack those players if you like there ratings and what they can do for you.
The recruits will commit at any point once you get your interet bar maxed out. Sometimes you will get some recruits to commit week 1 most of the time that isn't the case for me. Now you will have to recruit, recruit and recruit a little more. I like to push the players I want most the entire way unless I have a big lead and no future visit with another team. Do not let up once you get a soft verbal if another team is close to you and has a visit lined up the following week they can steal your player out from under you. I find it harder to steal from them but it can be done.
Once you build up your program at Rice you can recruit any player you want. You do not have to recruit a player who has interest in you going into the season. Now it will prolly be hard to gain 5 stars interest in going to Rice the first year or two. So look for those 4 and 3 star players who are really good players but don't have offers and go hard after them to build up your talent base.