Silver tarnishes, even fine (pure) silver. (Real) gold does not. A high grade (say over 10K) gold plate or filled chain, until the gold wears off a bit, should stay bright, apart from dirt/body oils/etc. All other metals tarnish as well, as far as I know. (That is one of the many reasons gold, platinum, etc. are valuable.)
However, body chemistry varies, and some people have more acidic sweat, which wears the finish faster.
I don't buy special chains new at this time, so can't offer a source apart from Rio Grande or Fire Mountain, the two places where I sometimes get quality jewelry materials. But if you can't afford gold-filled, which tend to be the cheapest of the options, maybe you aren't going to find anything there.