Why a headphone amp

Look around for a used Grado headphone amp. Get the battery operated one. A friend has one and loves it.

I applaud your inclination to "get some nice headphones." Personally, mine see far more action than my main audio system, as my wife is not an audiophile (imagine that). However, I have a long history of looking (and finding) ideal headphones. Your amplifier question has probably been well-answered by earlier postings.

My advice is simple: Try to attend an audio show. It will save you much frustration. They usually allocate a large room exclusively to headphones and headphone amps. Find the phones you like and invest in a quality headphone amp. Any of the phones you audition will be fine, but try to find one that you can live with long-term. I recommend Stax, but they are not for everyone. Good luck in your search.

Get a good tube unit they are cheap enough be a sport.Headphones will never take the place of a first rate setup.

For flexibility overall with headphones or speakers Bel Canto c5i is excellent all around digital integrated amp including for use with headphones. I have Sennheiser Momentum phones that C5i does a wonderful job with and it is all the hifi overall that most would ever need.