I had always sent my returns in certified mail until this year when a state return said sending certified would actually delay the process. Is there a best way to send returns for federal and states in general that do not explicitly say the best way to mail on their website?
If you send them well ahead of time, then you can be sure they arrived by having a copy of the cashed check you sent to the IRS, or if a refund was due - receiving the refund.
But if you're sending close to the deadline (March and later) - you might not receive the refund check (or your check might not be cashed) before the Tax Day, and you won't have any proof that you sent it. So, to avoid late fees and penalties, if you send 1-1.5 months before the due date or later - send certified.
It is a good practice, however, to send it certified always. You never know what might happen, and it doesn't cost that much more. The burden of proof that you filed your taxes, and did it on time, is on you.
The best way, in my opinion, is e-filing.
If you're submitting your tax return at or near the deadline, you can use IRS-specified private delivery services to meet the timely filing requirement. Your state's requirements may vary, so check with your tax or revenue department's website.
Some people feel that using USPS Certified or Registered mail gives you some additional legal protections, as US Code explicitly states that the receipt from such a service is prima facie evidence of filing. (Although it may delay processing, particularly with registered mail, which requires a written audit trail for every USPS employee who has custody of the letter)
I'd suggest that USPS Certified Mail is the cheapest way to submit your returns if you require documentation for a last-minute filing. If you care about processing time, file early via first class mail or e-file.