That will work fine with 6, 7, and 8 speed.
6 lacks some gearing for the downhills.
7 is optimal for speed vs price.
8 has the nicest shifters available and is just as fast as the 7, 9, 10, etc. . .
However the 9 and 10 speed shifting is hyper-sensitive, thus bring about a question of why you would even want to go that route.
SRAM PC 68 chain could be helpful (max 8 speed) because it bridges the compatibility between 6 and 8 quite easily with no errors. A Campy 8 speed chain is also very good. Avoid the Shimano/KMC chains because they eat gears.