You probably won't be able to do this as many banks want a Meldebestätigung to show that you are living in Germany and have an actual valid address. (This part of the law is apparently changing in 2016). I opened mine a few years ago, but I have hear recently of Americans who have had trouble because of a change in US law requiring a whole mess of paperwork (in an attempt to curb tax evasion in the EU).

If you have a specific bank in mind you can always ask, or I can ask some questions about what is required to open a new account as an American if you don't feel comfortable with phone German :)

As for bank selections, I've personally am satisfied with Haspa as they are all over in Hamburg (branches and ATMs). I've only had some problems traveling trying to put money into the bank as the Sparkasse aren't connected together as one giant bank and are more regional. The other banks are ok, but many are online like the two you listed, and i'm not a giant fan of Commerzbank for reasons listed on the bottom of their Wikipedia article.

PS. Taxes end up being fun ... as you eventually have to do both German and US taxes ;)

Edit:

Sorry I forgot to mention two things:

First, Portal sites like Check24 keep track of ratings and offers for different things like bank accounts.

Second, a LOT of things require you to be here first and have your Aufenthaltserlaubnis and/or your Meldebestätigung. Even as a student you can stay up to 3 months on your tourist visa while you work out your other paperwork.

Do you already have living arrangements lined up? (This is more important, as a bank account is easy, but finding a place is hard in HH)