It's easier to get great photos when you have the proper gear. The proper gear for shooting a hockey game at ice level is the 70-200mm F2.8. You need the F2.8 to shoot at 1/1200 second at ISO 1600. The zoom lets you cover a lot of ice. Everybody uses one. It's the easiest way to go.
I'm trying to mix things up a bit, mostly so I can give better advice to those photographers who don't have the fast zoom.
Most people can afford a 50mm lens. It's not a lens used that much for hockey any longer but there was a day when it was the norm. It gives you great coverage of goal-mouth action. If your child is a goalie, or a great goal scorer, then the 50mm is all you need.
The next longer lens is the 85mm. Again photographers used the 85mm for years for hockey. I remember one of the old timers shooting with an 85mm at the goal-line at Maple Leaf Gardens for years. It was the only lens he used. Most of them are F1.4 which is great for the darkest of rinks. It's perfect for goal-mouth with a full-frame camera and nice and tight with an APS sensor like in the Sony A500. For this shot I used the Zeiss 85mm F1.4 on the Sony. It's a great lens and wonderful at F2.8.
The lens I'm really enjoying for hockey is the Zeiss 135mm F1.8. It's so fast, the colours are great and it's very sharp at the working aperture F2.8. I take a lot of photos of players battling for position in the slot. I know they all look the same but isolated action is what I'm there to do. With the 135mm on the APS size sensor I can get a nice waist up of a player or a full frame shot of the goalie. It's just too tight for any goal-mouth action and I tend to miss a lot..... which is why people use a zoom lens for hockey.
This is with the Sony A500 and the 50mm F1.4.