It Depends on What You Are After
Your choice depends on what you are after and what water you will be fishing. For instance, on the York and Dartmouth the possibility for a 30+ white hot Springer is possible during the first week of June on the lower public water. For years I have chosen this timing because no other time of the year offers such a pure opportunity. This is also true of The Restigouche, Matapedia, Cascapedia. June first is possibly my favorite overall day of the calendar. Now that I have said this please understand that the odds are not in your favor. This is quality time and by no means a quantity situation.
The next timing in June is around the 10th to the 14th depending on late or early season as well as by river. A wave of 12 to 25 pound class fish arrive. There will still be some large fish and some grilse will be present. This timing up to the 21st can see the holding pools start to collect fish. These are bright and powerful fish. You will have a greater quantity of salmon, the water will probably be lower, and the weather is far better.
Now we move to the end of June into July. This brings a wave of fish of every size. Dry fly fishing is going well and stealth is of major importance. So long as the water and weather cooperate this is the most prolific time for salmon fishing. Please remember that if you are fishing public water the quantity of fish has a direct effect on the quantity of anglers. You are deep into kill season.
This process is happening on all the rivers of the Gaspe. The earliest starting on the Restigouche(Middle May) and later on the Pitite Cascapedia, Bonaventure and Matane.
I first started going to the Gaspe in 1980. I fish all the above time schedules on different rivers public, zec and private. Sometimes success sometime not, but never have I looked back without wonder. My comments are an in general guide. Each year on every river is different. You can only go with the odds of experience and roll with the decision. You are on the path to Salar nirvana in North America. If you can afford to use an outfitter or guide service I would highly recommend doing so. All the very best of luck.