It should run Leopard without any problem. the memory requirement is only 512k and I don't recall any Macs of around that period coming with less than that. The CPU is certainly fast enough to handle it.
TBH Panther should run without crashing anyway but the version of Safari at that time had a very early version of the rendering engine that could be temperamental so an upgraded OS X will have a better browser.
iTunes used to run fine though, at the time that Mac was current I regularly used iTunes to rip CDs to MP3 and play them back or burn them to CD without any problems.
What sort of crashes are you getting ? If they're OS crashes, causing a restart, rather than an application quitting, it may have a hardware problem, reseating the memory is always worth doing if you're getting random OS crashes.