For my pergola I caulked between each set of panels. I used clamps to compress the caulk and hold the panels during mounting. I didn't need them to be 100% water proof, but if I had, I would have added T-molding on the top between the panels in addition to the caulk. I only have one row of panels on my pergola so this was pretty easy. If I had multiple rows, this method would not work. So my advice would be to stick to 1 row of the longest panels you can get.
If, on the other hand you need/want multiple rows, you will need to go with a different method. You could add a trough/gutter between rows to collect the water from each row and move it to the end of the row. Alternatively you could use an under deck drainage system or hack one together your self using large sheets tin/plastic panels.
As far as tips in constructing the pergola, one of the mistakes I made was in using 4x6 lumber for the top beam. Not sure how it is around the world, but our lumber has slightly rounded edges and I was limited in the length of lumber that I could get. If I had it to do again I would have used either 2x6 or 2x8 lumber and cut off the rounded edges and then sandwiched multiple ones together (glued and screwed) to create the exact lengths I needed with perfectly square edges. In fact, I would have cut off all of the rounded edges on all of the beams. I noticed before putting the solar panels on that I was mounting them to a couple of stainless steel U rails (facing down so as not to trap water). I forgot to paint or even thoroughly clean these and they are somewhat noticeable so If I had it to do again I would have cleaned and painted them. I made sure to add pieces of rubber between the rails and the solar panels so they wouldn't corrode.
For what I did right and would do again, I used black decorative metal connectors between all members and at the base of the posts which turned out very nice (I had to paint some to match). But it was hard to paint the wood around the brackets so I would be sure to prime and paint before assembly (at least under and around the brackets).