Malta is one of my favourite holiday destinations. However, it's a bit like Marmite: you either love it or you hate it!
I wouldn't stay in Valletta, Sliema, or St Julian's. Too busy for me, with a very active nightlife which can make it hard to sleep. The buses are very reliable (plus when they're announcing the next stop, it's announced in both English and Maltese, which I found amazing!), and you can get a bus pass for the week for about 25 euros (and you can use it in Gozo too). The ferries from Cirkewwa run all night; I'm not sure about the routes from Valletta, etc. Mellieha and Paradise Bay have some of the only Sandy beaches, but in all honesty, in October it will be too cold for sea swimming.
Bugibba and Qawra are very British-oriented, but Bugibba has great transport links to the rest of the Island. Historically, there are loads of sites to visit. Gozo is less busy, with not as many hotels and not as built up. Absolutely beautiful scenery, and you can go Quad biking, etc if you want to. There are also Jeep tours.
I've stayed in both Bugibba and near Cirkewwa; I preferred the latter for the quiet at night, but preferred Bugibba for the easy transport links. That said, it wasn't exactly difficult to get around from where we stayed either, and we weren't too far from the Cirkewwa terminal for the ferry, which was a bonus.
Driving-wise, I'd take public transport over hiring a car at least the first time you visit, as Maltese driving can leave a lot to be desired, but on the whole the people are super friendly, and English, along with Maltese, is their first language. It tends to be the older generations who don't speak English as much.
There is a lot of building work and roadworks as they're updating roads that were badly in need of repair and getting rid of the potholes.
As with all things, it depends on why you're visiting! Me? I love the history, the food, the wine, the culture, and I have friends there too and would happily move there if money allowed!