Your best bet is to set up a DB2 for Linux, UNIX, or Windows server on a PC. I would recommend Linux, since the OS is basically free, and it similar to UNIX, which it the most common platform for DB2. Any decent PC can handle it, with memory probably being more important than processor speed on a development machine.
You can get a trial version of DB2 ESE for free (you have to reinstall every 3 months) from the IBM website. Reinstalling every 3 months is not so bad since it gives you practice with installations.
I don't know of any mainframe solutions that you can easily set up at home.
Of course, DB2 for LUW is substantially different from the DB2 for OS/390 and z/OS, at least at the DBA administrative level.