Browsers for Apple

[Braindrain]

My parents have a 6-year old Macintosh computer that has 2 browsers
in it: Internet Explorer (the last version that was made for Macs) and
Safari. IE is so outdated that all you get is the "spinning beach ball"
(Mac users know what I'm talking about). Safari (I'm not sure what
version it is) simply refuses to look up certain sites! My father will
be trying to get the link for our bank or his retirement fund or look
up something else and gets any one of these messages:

site not found

site does not exist

list of Apple sites that have absolutely nothing to do with what he's
trying to look up.

My mother gets the same thing, so it's not just him.

The bottom line is that we need a new browser for the Mac-something
that's easy for both of my parents to use. I've heard a lot about Firefox,
but I don't know anything about it. What other browsers are compatible
with Macs? This is really getting ridiculous!

Thanks!