I agree with you about the fact that Venice is the place which should not be skipped if one happens to be in the area. I also know that Venice may be expensive compared to other places.
Having said this, I'd surely go for a Venitian accommodation rather than one at Lido.
Venice is a town which should be enjoyed on foot. People do take vaporetti or motoscafi (gondolas are just for tourists, although you might like the romantic side of this experience), but most of the time they walk. By walking around, you get a better grasp of the place, you may stumble upon little squares (campielli) or areas which are not mentioned in guidebooks but which have a particular charme. And walking around in the evening or at night is fascinating.
If you stay at Lido, you are forced to rely upon boat service to move between Venice and your accommodation (if I remember correctly, it takes between 30 minutes and one hour to get from the train station to the Lido according to the route, and it costs 7 euro one way), which would limit your wandering possibilities. Lido is a seaside resort, a bit on the classy side but no longer the kind of place Luchino Visconti described in his film "Death in Venice". It is certainly worth a visit but it does not represent the most meaningful part of Venice.
If you decide to stay in Venice, you could look for accommodation in sestiere Castello (sestiere means quarter, neighbourhood), an area quite close to Piazza San Marco but which has retained a more popular character. If on the contrary you prefer to sleep elsewhere, I would recommend staying in Mestre, because you can easily get into Venice from here either going by public buses or taking any train which ends in Venezia Santa Lucia station (the journey by train between Mestre and Venice is under 10 minutes).
EDIT: I have a doubt: when you say that accommodation seems to be much cheaper in Lido, are you perhaps referring to Malamocco or Punta Alberoni? These areas are certainly on the Lido island, but they are further away from the town of Venice, towards the southern tip of the island itself, so you would have to catch a bus first and then the boat into Venice. They are seaside resorts, so October would be low season for the hotels there.