The best browser for everyday use, and particular for homebanking is OPERA. It's the best browser and it's also multiplatform Mac, Windows, Linux and may others.
I tried FireFox, Mozilla, Camino, Omniweb, Safari, Netscaper and IE. IE is the most compatible one, but now it's abbandoned, some of the other are fast but not compatible with homebanking, particularly those based on apple' webengine. Some others don't work well and are only web blasoned browser. The one that is fast and works very well on mac and pc is Opera. Also the most of the others, except IE, has problems with javapages, Opera works fine and very fast with java. I hope other browser could reach the same features and compatibility of Opera but Mozilla and Firefox are still not usuable for the everyday work. Use it at home but exclude a lot of features and homebanking websites.