I took a day-trip to Sarlat in early June on a miserably rainy day. There were quite a lot of tourists there even then (it was Wednesday, a market day), but it was easy to see that it is ordinarily much more heavily visited, because nearly all the (many) restaurant tables were empty. As I said, it was a dreadful day, weather-wise, and anyone with a car would have found a more indoor-oriented destination for the day. So I'd class Sarlat as very touristy during peak season. How much better it will be in October I do not know. However, Sarlat seems to be the most popular base in the area, so you should not expect an unspoiled town.
But it is lovely, and it's large enough to offer a lot of options for dinner. I would rather stay there than in one of the tinier places. However, I depend on public transportation (making Sarlat not ideal as a base for me) and do not like to be pinned down in a small town in the evening. I especially would not like it in the Dordogne because I do not eat the local favorites (foie gras and confit de canard) and need multiple restaurants to choose from. For other travelers, having lots of restaurants and good public-transportation links would not be so critical. Those wanting a less touristy environment might be happier in one of the smaller villages, assuming they are traveling by car.
Even on an extremely rainy day, there were lots of market stalls set up in Sarlat on Wednesday. I'd recommend that market if your schedule doesn't allow you to be in Sarlat on Saturday.