Everyone here has definitely given you some good advice. As Deb mentioned, the chain line will undoubtedly be better with a new crank and bottom bracket.. and then of course you'll also need a new front derailleur. However the other problem is that a compact double is made for 9/10 speed rear wheels... which means it needs a much narrower chain than your current 6 speed rear wheel.

Another choice is to check on a touring crankset.. they usually run 50/42/30 but you can also get 48/38/28... so you definitely have plenty of options. This make work out better for you in the long run..

Good luck!