Fran, if you loaded 30# onto each end, you were actually squatting a lot more than 60#! An Olympic bar (standard size) is 45#, so if that's what it was, you had 105# on your back.
You don't want to put the bar on your neck! It goes on the top of your shoulders. I seem to have a natural spot that the bar fits into pretty well (an inch or two down my back).
It's hard to make out, but can you see where Mr. ExRx has his bar?
But I can't put the bare bar on my back either - it's painful and I get bruises too. Fortunately, the answer is easy and costs about $10 - 20:
It's a squat pad - a cylinder of dense foam about 4" in diameter and 14" long that velcros around the bar. Once it's on, you duck under the bar on the rack and settle it on your shoulders - no pain! No bruises!
When you describe
one of the squiggly bars that has the neck portion angled out, I'm not sure if you mean an EZ curl bar:
or cambered bar:
But either way, that's not what you want for squats. Try a squat pad instead. I have my own personal one that I carry around in my gym bag.