Chains I would say are probably the most secure lock you can get, they are probably the most angle grinder resistant bike lock one can get
The problem is that they are really hefty and I don't really know how I can bring one along. Also they don't really attach to your bike so transporting them is really not that fun. I guess I could just leave the chain at the bike locking structure, I hope it doesn't rust or something because it is quite rainy here in Vancouver.
Big, hefty chains like the Kryptonite are where it's at, but you're right, they're heavy.
Cruise around Manhattan, and you'll see a lot of heavy chains sitting on the ground wrapped around posts. Some people tend to buy multiple chains and leave one at each place they intend to park their bike. Personally, I don't care for this approach. In addition to being expensive, it means that I can't simply decide to go somewhere new on a whim- I'm locked (pun intended) into a certain commute path every day. Though to answer your question- the higher-quality hardened chains tend not to rust at all- just be sure to keep the lock itself clean and well-lubricated.
I carry mine with me. If I'm feeling particularly heroic, I sling it over one shoulder and around my chest like a bandolier. It only weighs 8.5 lbs, and all the cool kids are doing it:
I've also seen a few people wear their chain like a belt around the hips. Protip: if you decide to do this, do not lose the key.
More conveniently, however, I have a wire basket on the rear of the bike, and if it's not filled to capacity, I simply toss the chain into this. If you lack a basket, get one. Not having to wear a backpack on those warm, muggy summer mornings is worth the $30. If you still don't have a basket, you may be able to wrap the chain around your handlebars, or around the forwards triangle, depending on the size.