I am also going to visit the Valencia tournament this year (for the first time) and I can understand your trouble with the website.
My friend and me also needed a while to understand everything, but we have booked our tickets now and will pick them up in an "El Corte Ingles" when we arrive in Valencia.
As this is also my first time to visit the Valencia tournament I can´t tell you for sure if you can buy tickets the same day or not. Last year Rafa was supposed to play the tournament, so I guess that might have influenced the ticket situation last year.
I would always buy the tickets in advance, just to be 100% sure. It wouldn´t be so much fun to travel to Valencia mainly for the tennis and not being able to enter the venue. I would, in your case, try to book via the website again.
You have to buy tickets for each day and session (day and night session from wednesday on) seperately, so you get lots of confirmation.
Hope I could help you at least a bit & wish you a great time in Valencia already