Else here fro the lumber business. I used to own the Morning Wood Lumber Company.  

 
To answer your question, if you need to be screened because you haven't seen her before, I suggest 3-5 days. If she knows you, then 1-3 days before the date you want. If you book too far in advance, there is a much bigger chance that something will come up in the meantime that would require one or the other if you to cancel before the session date.

... a date scheduled well in advance yet. I like to schedule 2-3 weeks out because my calendar is tight.  Most providers I've asked to meet are fine with that, but some prefer booking no more than a week out.  Usually those providers have another job for which they know their schedules only a week in advance.  

If you do book a few weeks out as I do, my advice is to touch base with the provider a week out, and then the day before, to reconfirm.  Most providers I know are great at letting me know if something comes up, but I've found it helps to keep in touch.

When it comes to making an appointment, I like to book with someone a week in advance, maybe 2 if my calendar looks firm.  I've tried the booking for next day appointments, but that gets a little too close for comfort with me.  Waiting 5 hours to get a 'yes' to an appointment request for the next day drives my Rain Man autism batshit crazy.    I'll do it if the conditions warrant, but I don't like to.  
   
But you seemed to really ask about screening?  Screening is different.  I like to screen with a new lady 2 weeks before I want to see her.  This gives her time to hear back from my references or get to know me a little better over an email thread.

and time, I will schedule several weeks out. Once the date is set I will confirm with a quick email about every week or 10 days with the final confirmation 48 hours in advance of the scheduled date.

If I know I want to see someone on a certain day but my time is more flexible, then I will wait until a week or so in advance and set up the date. This still gives me time to go to plan B if provider A is not available.  

Also, in either case, if this is a new lady to me, she has plenty of time to check my references.