In DE from 1/5-most likely, there will be a ALL GERMany=DE LOCAL monthly season for just 49€-as subscription. Name is Deutschlandticket-on sale from 3 - 4 (EU-dating!) and also covers all bustrammetro-much more fit for such local travels.. And I assume that a student does not go there to only travel all over EUR. There MAY be a MIN term to buy it, but even if this is for 6 month it will work out as a very good buy.

One could indeed consider buying an EUrail for a certain nr of days=much cheaper and use that for some trips to grab the chance to see more as only DE. It will all depend on exact city what is then feasible for weekend or the like. But as one can alays buy that pass in an instant there is no need at all to do that monthes ahead. DE has the advantage that as such all ICE/IC trains (that DE-ticket is NOT=nicht valid on them!!) have only optional RES and if wanted this can be done in a few secs via the bahn.de site.

A continuous Global pass would allow you unlimited travel across Europe throughout your stay, but require some reservations on high speed trains. It is ideal for those with plans to wander freely across Europe. 

The 49 euro monthly pass will allow unlimited travel on all German regional trains and most buses and city transport. So they complement each other with the overlap of German regional trains.

The 3 month pass cost about 770 euro so would only be worthwhile if you intend a lot of weekends exploring Europe on long distance trains, otherwise, as well as the proposed monthly pass, most German states have a range of passes.

A bit of research on your aspirations and your budget will no doubt show you the best way forward.