Finding the right length of chain lock for my road bike
I faced the same dilemma a while back.
Getting a big chain implies carrying way too much weight around. Even a small, good bike chain is pretty heavy and can easily be 1/3 the weight of your bike.

The best way to protect your bike and be able to carry the locks around is to have a chain or a U-Lock, and with these you can easily secure your frame and a wheel, and then use a small cable like this to secure the other wheel. One wheel is less protected, but a substantial part is under a good lock and the weight is not too bad.

From these I actually prefer a small chain to a u-lock because it is easier to lock the bike to a tree for example, but if your city is bike friendly a u-lock offers very good protection and is much more manageable.

When buying locks keep in mind price usually means security. I recommend you check the independent tester of locks Sold Secure. They have a catalog with different locks they have rated.