Those are the old-style cylindrical keyed locks U-locks, they haven't made those in years.. but yeah- I'd avoid buy old used U-locks.
New locks have a redesigned straight flat key system. Just be sure to use a lubricant (chain oil or such, not WD-40) to keep the lock from rusting and seizing and breaking your key off!
I couldn't break the U-lock (it's a U-lock and a high-grade steel chain?). I could probably bust that chain off (chains are vunerable to prying and cutters- they have seams). I hope you're locking the U-lock to your frame to whatever you're locking it to and not locking the chain around your frame only- just to be sure. It also goes without saying that your locking is only as good as what you're locking it to..chose metal (thicker the better- in full public view Vs. smallish evergreen shrubbery behind the mall?
Also, you don't need to buy a brand name Kryptonite U-lock..they're $10-15 more and it's just a brand name! I have a Bell that I got for $14 and it's been used for years..
I have three Kryptonite chains. One is a NY FUGETTABOUTIT chain. I misplaced my key, and the maintenance man took 45 minutes to cut thru it with a grinder (I gave him $10 for his troubles).
At work, I run the chain thru three bars on the bike rack, then thru the rear wheel and rear frame. A cable runs thru the front wheel and frame.
I secure my bike on the fourth floor of a parking structure, and it's relatively safe. My co-worker lost her highly desirable Honda moped on the third floor. It was chained, but not to a pillar or anything. At home, I keep it in the house, bungeed to the wall, so the dogs can't knock it over.
I leave a Kryptonite chain and a cable secured to the bike rack at work. That way it's there waiting for me at all times.
I claim the only bike rack in the building, because I'm the only cyclist out of 200 State and TV station employees.
That's sad.