put the chain in the two largest sprockets i.e. the big ring at front, and gear 1 at back and check that the rear mech isn't strecthed too much (you shouldn't ride in this gear anyway, but it's worth checking. the thing to look out for is wear, if the chain is worn, then there is a chance the sprockets are too so a new chain might not 'mesh' properly. the more expensive chains are usually slightly stronger, and shift a little better. the pc971 is a pretty good chain, it seems strong, reliable and durable.

any 9 spd will work with each other i run a pc971 on a shimano deore cassette, just go with what you can afford with the gear ratio that u want. a good bike shop will measure the chain for wear and let you know if u need a new one