Lausanne will have more hotels, more restaurants and a bit more to see including more life. Montreux is very family oriented and won't be all too lively at night except for the 18 year olds who go out at night.
Lausanne is a great base and is only 20 minutes train ride to Montreux. But don't discount montreux as it is so beautiful and walks at night along the water are wonderful. I even lived there for 1.5 years and I'd still recommend Lausanne over Montreux.
Montreux and Lausanne both get you to Gruyere for your cheese and chocolate tours.
Montreux is nice and you will be at the end of the tourist season. There still might be boats running but not too much longer after September. The waterfront in Montreux is wonderful and you will want to check out Chateau Chillion. There are some great little trips above montreux on a cog train to Glion, Les Avants and les Diablerets.
For Matterhorn, it will be 2.5 hours from Montreux. Just add 20 mins to that from Lausanne. The first part of your journey into Sierre will be quite fast, about 1 hour. But then you will take a cog rail up to Zermatt which is very slow - giving the 1.5 hours ride. It is so scenic and wonderful that you probably won't notice the length. I visited Zermatt in September, it rained but we hiked and I loved it. Not too crowded.
I'd also check out Bern, Vevey and Nyon on your travels.