what kind fo chain does the bike currently have? 525? im pretty sure thats it. anyways, going down to a 520 is fine on a 600, on liter bikes usually not such a good idea since the strength of the chain is usually lower. but like i said, youll be fine.
x or xw is def the way you want to go, they will last much longer than o-ring chains. rk is what i usually sold the most of when i worked at this one bike shop.
as far as sprockets go, get steel, all around. your front will most def be steel, the rear you will probably have to search for steel as aluminum will be everywhere. the weight difference is not going to affect a street bike and the aluminum sprockets get torn up very fast. check forums to see what ppl say with gearing with your particular bike. rule of thumbs is 1 down in the front is the equivelant of 3 up in the back. so its like your going 5 up in the back, will def still be ridable but like i said, do some reseach on ur specific bike.
oooh, and get a rivet master link, not the clips type, those are dangerous.
if you dead set on doing it yourself and you cant get the tool to rivet the link, buy a snap link, put it on, ride it to a shop and give them the rivet master link and have them do it
thats about it, all of this i picked up from working at a shop for a while just after i moved out here