I ship my clubs all the time. I've tried a lot of different things, but the most important factor is where you are going from/to as the costs change based on that and the providers. 

Personally, what almost always works out best for me is to ship using a Fedex box (15x15x50 only costs $10 from the Kinko's Fedex store) and I ship using my UPS account (doesn't matter that the box says Fedex on it). I get a better deal through UPS for shipping. 

I almost used www.luggageforward.com once. I found a discount code by searching around a bit, but round trip ended up better with UPS. Since you're only going one way you should check that as well as Fedex and UPS. 

Last option is to ship just your clubs in a club shipping box (without the bag). You should be able to get one from any golf shop and then just send your bag with the moving truck. 

Best of luck in the move!

Ben