Welcome to the forum.
You are right, there are generally two schools of thought on this.
There is no right or wrong way to do it...so it's not something that can be easily answered for you. You will probably have to try some things and see what works best for you.
To add another variable (and make it more convoluted

) let's throw in the issue of selling the digital images. These days, a lot of clients want the digital images...and a lot of photographers offer them. There are pros & cons to this (as with any issue) so it should be carefully considered.
On one hand, you can sell them, then not have to worry about reprint orders to make money. But you have to sell them for enough that you make enough money on them in the first place.
If you let the clients order/make prints themselves, you loose control over the final product. They might have them printed at Wal-mart and get bad prints...then blame you. If you sell the prints yourself, you can make sure that they are of good quality.
The same issue still applies...do you charge a lot for the sitting fee and less for the files/prints....or do you lower the sitting fee and charge a lot for the files/prints.
Personally, I have changed my structure (or at least changed my thinking) a few times. For a while, I liked selling the sitting fee and files (on CD) for one price. I included a set of 4x6 prints, so that they knew what good prints look like. This was good because once the product was delivered...I didn't have to go back and forth with them, over and over again....waiting for prints orders etc.
On the down side, you might loose contact with your customers...and they might not be so quick to call you up again.
What I'm planning to do, is set up an on-line ordering system, where I can have clients order prints on-line. This will mean more work for me, fill those orders, but I think I can make more money this way...and it also allows other people (family members etc) to order prints from the shoot. I will probably still offer the CD of image files...but I will up the price of it. This might also allow me to lower my sitting fee (but not too much) which might entice a few more customers. If I were more in-demand...I'd keep the sitting fee higher and rise it as often as I could get away with.
To take the on-line ordering a step further, there are some great sites that will handle everything for you. You just upload the files after the shoot...and clients can order from that site. Their orders are filled and shipped...and you just sit back and wait for the money to arrive. Of course, these sites do get paid...it's usually a monthly or yearly fee plus a percentage of the profits.