To answer this question I'm going to look at the 2003 NetPro Serena Williams rookie cards, Serena's first true official trading cards. 

The short answer to this question, is NOT VERY MANY. Even the largest batch of base rookie cards had only a 40,000-card print run. To give you a comparison, PSA shows almost 25,000 GRADED Tiger Woods 2001 Rookie cards. So you can imagine how many ungraded Tiger cards are actually out there in total. At the time of this writing, there are only 2500 graded Serena base rookie cards.

NetPro did a fantastic job in 2003 with tennis products and delivered several versions of Serena cards in varying production runs. The very rare numbered cards are of course the easiest to figure out, so I'm not going to focus on the /100 /500 cards here. I will also ignore the other inserts as well, since it's assumed those are also very rare.

It's important to note that the numbers here are the same for Roger Federer's rookie and Rafael Nadal's rookie cards as well since they were produced in the same quantities.

2003 NetPro Premier Edition

This is the base set of cards that NetPro produced. The print run for this set was 40,000 cards (#d 1-89) and then the short prints (#d 90-100) were obviously fewer. According to NetPro, the short print runs were 5000.

2003 NetPro Glossy 5000 Series

This set was limited to 5000 glossy prints that mimicked the Premier Edition base set for each player. So already you're down to a max of only 5000 of any player. These are numbered with a G in front of the number. Rumor has it that someone bought 1000 of these sets that were later discarded, so there may be only 4000 in existence. (This means the International Preview insert cards in this set is also down by 20% as well.)

2003 NetPro International Series

The stated print run for this series is 10,000 cards. So 1/4 of the Premier Edition production run. 

2003 NetPro Elite 2000 Series

This is considered the most significant NetPro release from 2003 as it is limited to only 2000 cards for each player. In addition the /100 Elite Glossy inserts were found here.

2003 NetPro Elite Event

Th numbers for this set are a little confusing, as NetPro states at least 10,000 cards were made. It's more rare than the Premier Edition cards but it's tough to say what the exact number is.

2003 NetPro Elite Event Starter

I had trouble finding much info about this so finally just contacted NetPro and the print run on these was said to be 5,000.

2003 NetPro Photo Set

It appears 10,000 of each card were printed for this set.