We have been to Venice several times, including all of October one year. It is still very crowded at least until mid-month; after than the crowds diminish a bit, at least they did in 2013. But things are different now, and people are traveling later and later into the month, so I strongly suggest buying advance tickets to San Marco for sure, and also to the Doge’s Palace Secret itineraries if you want to do that. A timed ticket for San Marco will save you time waiting in line.
For San Marco, it appears the tickets go on sale in blocks of full months. Right now they are offering tickets for only June and July, but I don’t know when those dates actually opened up. Most of the time slots are gone for all of June; towards the end of July there are some afternoon slots left.
So I suggest you start looking around the end of July—-in case they release the September-October block August 1. Or start looking now just to practice, as the site is not very user-friendly. You want to figure it out before you are under any time pressure.
Use only the official booking site, which is this (it does look strange, but I assure t you this is real—-they contract with. Norwegian company to handle ticket sales
https://basilicasanmarco.skiperformance.com/en/store#/en/buy?skugroup_id=2524
I recommend the “Basilica + Museum” ticket which will allow you to go upstairs to see the original bronze horses brought from Constantinople in the 3d or 4th Century AD. You can also go outside on the terrace overlooking the piazza, among the stone replica horses. I never tire of doing this, so we go on every visit.
If you want to see the Pala d’Oro there is a ticket that includes that as well—-your choice. I have never seen that.
Timing—-they turn on the lights to illuminate the mosaics around 11:30 (for an hour, I believe), and that is a nice time to be upstairs in the museum, close to the ceiling. This is nice, but if you want a less-crowded time to visit, go at the earliest slot, 9:30. We did that last October 1, and I really liked how empty the basilica and especially the museum were.
Another thing I highly recommend, although you did not mention it, is visit to the rooftop terrace of the Fondaco di Tedeschi, a high-end department store right by Rialto Bridge. You get a wonderful view of the Grand Canal right where it turns. The 15-minute visit is free, but reservations are required, and you must book them the day they are released because it is very popular. Do not be late for your appointment.
https://www.dfs.com/en/venice/mobile/service/rooftop-terrace
They release the reservations exactly 3 weeks to the day ahead of each date, sometime after midnight. But that is midnight Italian time, which for those of us on the west coast it is in the late afternoon or evening the previous calendar date. The slots go quickly, especially the late afternoon times.