Any mac computer ppl? I need help.

i had an older system running on my mac latoptop- OSX 10.3.9 and it wasn't compatible with many new programs, including the internet server program at my graduate university so i could never get online while there. became too much of a pain so i gave in and bought the new Mac Leopard 10.5.4

I'm such an idiot with this stuff. Before I install leopard, do I have to restore my laptop? If so, how do I do that?? And I should back everything up on DVD discs beforehand or something, right? or else id lose everything i have saved on here?

TIA!!