How do I secure a new bike outside my apartment?
Matt, this has got to be one of the most asked questions on here, have you searched through previous questions yet? That should give you some decent ideas.

All I will add is that you mention insurance. Your insurance company will likely have a list of approved locks - I'd suggest its going to be far more worth your while to consult that list than to ask a question on SE (much as the advice here is generally very good!). My betting is that the insurance co's list will contain big, heavy, hardened chains, so yes, the chain would probably be worth the weight (and the cost) if it means the difference between your insurance paying out or not.

Also your insurance will probably stipluate that the bike gets locked to something "immovable" - might be worth seeing if you have anything that might fit the bill in your basement, if not seeing if you can get permission to sink an anchor. I have heard stories of people locking their bikes to a bike rack, only for thieves to unbolt the bike rack from the floor! You may also want to find out whether your basement is considered a "public place", from the ins co's perspective, because they may place limits on the amount of time a bike could be left there. And, if its left inside, whether that would change things.

The sad fact is that if someone decides they really want your bike there's probably not a lot you can do about it - try not to get too attached to it, it's just a chunk of metal after all, and make sure you take sufficient steps that you will be compensated in the event of theft. 

I suggest you go read some policy requirements.