Any evidence of a date when you began using the mark in commerce would suffice. A printout of the website would likely work, but if you print it out today, how does that help you since you mentioned that you had been using the mark for several years? Hopefully you will have some invoices or other dated materials that can verify the first use of the mark -- otherwise, you might be able to use more circumstantial evidence.
As far as what is "sufficient" it depends on what you want to use the "proof" for. If you are trying to prove that you used the mark before someone else, then you need to have "more" proof than the other person that you started first -- preponderance of the evidence. If you are seeking to invalidate or otherwise challenge a registration of a mark through the USPTO, the proof level may be higher. If you are seeking to register your own mark through the USPTO, the proof is likely lower. It all depends on what you are seeking to accomplish.
Are you in danger of being sued, or planning to sue someone else? If so, then your attorney can give you more specific information based onthe actual facts of your specific situation.