My student loans and my wife's student loans got sold a few times, so the way it works kept changing.
We used the auto-debit for the interest rate reduction. Interest is compounded, so anything to lower that interest rate is a good thing. Then we paid extra. I don't recall there being a way to make the payment amount more, so we just made additional manual payments.
I like the manual extra payments because it gives us the flexibility that if things change, like a job loss or a car emergency or something that alters our financial situation, we can simply not make an extra payment for a while and then go back to it.
I do remember it being a hassle to make the extra payment count the way we wanted to. My car loan and mortgage allowed us to designate additional payments as principle-only, which was really nice because we could pay down our loan even faster. Our student loans, however, always applied extra payments towards pending interest first (even if it's only a few cents or dollars so far), then the rest went to principle.
We both started with Federal Direct Loan and their site did not have a way to make an "extra" payment unless we called customer service. An extra payment simply was an advance on future payments. My first year out of college, I got a nice tax refund and put the whole thing into my student loan. Guess what? I was off the hook for 6 months because they treated my payment as 6 months of payments. Argh. I didn't think much of it or care at the time, but in hind sight, that was not in my best interest.
Then they revamped their web site, maybe in 2011 or 2012. This provided a way to make the payment not count as an advance. It still went to outstanding interest first, but at least I could make an extra payment that was actually extra.
Then they sold my loan to MOHELA and that was a nightmare for many other reasons. I don't remember it very well because when it happened, I paid the whole thing off as quickly as I could to get away from them.
My wife's loan got sold to a similar company and they only handled extra payments as non-advances if you called and spoke with their customer service, which was staffed with people who didn't know what they were doing and gave incorrect advice (I know it's incorrect because calling back a week later and speaking to somebody else yielded a different answer).
Also, if you are only paying a few dollars extra, be careful about when you make the payment. Interest accrues daily, so if you make a $5 extra payment a week after you make your auto-payment towards the minimum, that $5 may just go towards next month's interest. Try to make your next payment as soon after your auto-payment as possible - the next day, if possible.
Start with the auto-debit because that is a free interest rate reduction, then make extra payments (not extra money on your payments). Making the extra payment count as an extra payment may be a hassle, but it can be done and you should do it.