Should I invest in a barbell weight set, or a bunch of dumbbells?

I'm an avid runner and my coach recommended weight training (in moderation) to help increase over all muscle gain. As a runner, my legs are well built/toned, but my arms and upper body leaves quite a bit to be desired. I'm trying to decide whether to invest in a $160 weight bench w/100lb weight set, or buy $160 worth of dumbbells. I'm a small woman, by the way. I'm 5'1, 110 lbs, but I can bench around 70 lbs, on a good day. Which would help me most in terms of my arms and core? Which is more versatile?
Should I invest in a barbell weight set, or a bunch of dumbbells?
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