You should be fine with MTB tubes. As for tires, read the markings on the ones that are mounted. They definitely make them in that size still (whatever it is), but depending on what they are, they could run anywhere from "dirt cheap" to $35.00 per tire. Not sure what else you'd be looking to replace. I'd start off by checking everything, and re-lubing the headset, bottom bracket, and hubs - and consider replacing the bearings. Hopefully there won't be much more to it than that.
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