Sorry, I don't have time to address this in detail any time soon. Just a few specific criticisms on points you may be missing:

1. OO modules generally should not use Exporter. The correct class that calls are to be dispatched to should be decided by the syntax of the method call.
2. No strict.pm. I can tell from your variable usage that you have the good habits it is meant to encourage. However it is a lexically scoped declaration and needs to be in a module for you to get the typo checks. (I list this after Exporter because I like putting Exporter related stuff before I use strict.
3. Your constructor is designed to be called as a function. This is probably connected to your exporting it. But that isn't good. You are overwriting the generic function name new() in other namespaces. Here is a much better constructor:

   sub new {
     my ($class, %self) = @_;
     return bless \%self, $class;
   }
   [download]

4. You are using full tabs for indents. It is important that indents be 2-4 spaces. You might be solving this by using custom tabstops. This helps you, but custom tabstops that differ between people cause their own potential problems (try programming in Python to find out what). I prefer using explicit spaces. (Easy with any decent programming editor.)
5. You have a lot of Student::get_attr() calls which are bad for two reasons. The first is that you are in package Student, if you meant to write them as function calls they are better written as get_attr(). The second is that they are actually all method calls. To move from doing OO lipservice to taking advantage of what OO does, it is important to switch syntax to $obj->get_attr(...), it isn't just that the syntax is "right", it is that you now do a method dispatch on type without scattering the assumption about type in your code.
6. You localize $_ unnecessarily. Having been bitten by something like this before, I sympathize with paranoia. But just in case you didn't know, Dominus's tutorial Coping with Scoping mentions the autolocalization in loops.
7. You have certain code which you write again and again. If you find yourself doing that (or cutting and pasting), that is a sign that you really wanted a function. For instance you write the same 5 lines over and over again for a random letter. Don't. Write a 5-line function and call it.
8. On a related note, you don't appear to have yet made the jump from, "this is how I will accomplish a certain kind of task" to saying, "I am going to factor that out by writing an interface to accomplishing this task". That is how you should handle your logging issue. Write an interface to sending log messages, and then call that interface. Decide later whether that goes to a file, STDERR, or whatever.

OK, I know that is a lot to digest, but I am going to give you one more item. It isn't Perl specific, but Code Complete is an excellent book which I think would be an excellent next step for you. It is mainly about procedural programming, yes, but the things it teaches are generally applicable, and will give you enough foundation in the principles of good procedural design to see what problems OO addresses.