If you are replacing the chain replace the cassette with it. Those two things drive and wear together. Tubes are cheap and arn't a bad idea even if the others seem to be okay.
Yes i agree, replacing deraillure calbes will help and housing even better. Also check the deraillure alignment to see if the hanger is bent and needs re-aligning. Check your rims are straight, if they are not, you will need to get them 'trued' up. Also spin each wheel and see how the hubs are performing, if when the wheel spins it dosn't spin very smoothly, a hub service could be in order.
If your chaning the tyres I can recommend the Panaracer or even the Kenda Nevegal. But there are HEAPS of tyres out there, leave this deciding for last after you've fixed up the rest of the bike!
Good luck.