The easiest way to understand Lago di Como would be to look at a Map (there's a good Map in Rick's Italy book). However, here's a brief description.
Lago di Como is a long, narrow lake shaped like an inverted "Y". The city of Como is located at the bottom of the left-hand leg. Bellagio is located about the center, on a peninsula where the "Y" joins (if that makes sense?). There are small towns and elegant old Villas located all along the lake.
The city of Como is has perhaps not the best place to enjoy the area. Some of the other towns are better to enjoy the "charms" of the lake. Varenna is a favourite with many here, as it's well covered in Rick's book. It is indeed a great place to relax and enjoy the area (and of course some Gelato).
Bellagio tends to be a bit more "upscale", and you could certainly stay there as well. The quickest way to reach Bellagio is via Ferry from Varenna (about 20 minutes). You can also travel there as a "foot passenger" for a day trip if you base in Varenna.
There is at least one lakefront Hotel in Bellagio, the Grand Hotel Villa Serbelloni. It's been owned by the same family for five generations as I recall, but one important point if you choose to stay there - be sure you have a LARGE budget!
Varenna also has many good lodgings and two old Villas with beautiful gardens that are open for touring - Villa Cipressi and Villa Monastero (buy a combo ticket to tour both).
It's very easy to reach Lago di Como by train from Milan. If you'll be staying in Varenna, it's about a one hour trip. I don't see any need to rent a car for that part of Italy. Others here have commented on the narrow roads along the lake, which can be challenging.
Some of the "rich & famous" have Villas on the lake. On my last visit, one of the favourite activities at dinner was trying to guess where Clooney's villa was (we had it narrowed down!).
Cheers!