Hi Susan,
I just stayed at Caulaincourt for four nights and had no problems. There isn't really any security: no lockers, you just leave your stuff in your room. Take valuables (money/passport) with you or leave with front desk. I carried mine with me. But I think that the fact they don't have any lockers tells that they don't really have a theft problem (just a thought). The hostel is fine, lots of stairs, and expect to spend 30 minutes checking in - they are super-slow. Follow Hostelworld directions to find it - they are really good. I met some great people at the hostel, I think that's the most important thing. Plus, they have a very nice breakfast.
Paris is beautiful, you will fall in love with it. 3 days may not be enough time to see everything you might want to see, but you'll be able to cover a lot. At night, buy a cheap bottle of wine at a mini-market (2.5 euro for 500 mL), ask them to open it for you at the store, and go sit on the Sacre-Coeur stairs with your buddies from the hostel. You'll never want to leave.
Where are you staying in Amsterdam?