When would the best time be to book this tour when the attractions are not so crowded.
Probably November, January and February, though Venice will be very crowded in February 2020 from about the 10th to the 25th because of Carnival.
I have done them in two trips - one from Oct 1 - Oct 17 and the other from Oct 12 - Nov 1st. Didn't notice much difference in the crowds, but the weather was much nicer (no rain) the first half of Oct. Had reservations for all our attractions and went to them early as possible to avoid the majority of the crowds! You will love it!
Venice tends to flood in the Winter.
We have been to Italy several times. I think October is still a great time to visit. The weather is still nice and crowds are not like Summer.
I agree that October is the best time to go for pleasant weather and lighter crowds. I went on the RS Best of Italy tour from early to late October. Sunny days and mild temperatures. We did experience Acqua Alta in Venice, the only place that rained the whole time we were there. But Venice was still wonderful! That’s the chance you take.
We took this tour in mid April and it was fine as far as crowds. Vatican is probably always crowded.