Yes, but you need new corks and a corker tool of some sort.
If you have a recycling center you can typically pick up all the wine bottles you'd ever need there.
As to reuse, when I first started making wine 5 years ago I bought 24 new bottles and have reused them each many times. The labels that come with wine kits are thankfully a lot easier to remove than many commercial bottle labels. A good soak in oxyclean will normally get most of them off and the ones that don't come off easily get recycled.
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