Hello Dick!
Welcome to JEvents :-)
you can do all that with RSVP Pro. So the user registers and then is push to Virtuemart to complete the purchase. On payment confirmation the user can view the ticket in the Event Details at which point they can print it off, it's a QR Barcode.
Then you as the administrator, login to the website on your device usually a phone, and then just scan the barcode to confirm the attendance.
I hope that helps!
Many thanks
Tony