chris,
Each of us here has a favourite of the five towns, and I prefer Monterosso. It's the largest of the towns and therefore has the greatest number of hotels and other facilities, as well as the best beaches. At the end of September / early October the crowds should be starting to thin-out a bit so it should be quite pleasant there (providing the weather is good).
I don't use apartments for a couple of reasons. To begin with, usually travel solo and I prefer to use hotels so that I can get help from staff if I need touring directions or whatever. It's also nice to have other people around to chat with. I also like a place that provides a full breakfast. Apartments are not a good fit for me as that means I'd have to shop, cook and do dishes and that is NOT going to happen when I'm on holidays.
My favourite place to stay in Monterosso is Hotel Villa Steno and that's one I would definitely recommend. If you have the RS Italy guidebook, there are lots of other hotel listings there.