Chain: Sram PC971 will be good enough.
gear cable and outer don't cost much.
Cassette: Shimano Deore will probably be better than what came with the bike
Chainrings can be expensive. See how worn they are. If you need a bottom bracket too then you might be as well getting a whole new crankset.
Jockey wheels should have a bit of play in them. Only replace them if they are worn RIGHT down.
To do the work you will need some basic tools. Chainwhip, cassette removal tool, chain tool. Bottom bracket tool, cable cutters and allen keys.
Take the bike into a bike shop for an opinion and take it from there. I replaced all the above parts [more or less] on the other halfs bike for c£120, and thats with me doing all the work.