Hi there, 

>I recently pulled an old hp9000/300 out of a trashbin
>and am now wondering which model it is.
>On the back it says model: '98563' and inside are a 68020, 68881 
>and a 68851 (MMU?) - I expect it to be a 330 ?!?
Yes, the 86851 is Motorola's standard MMU
Hmm, maybe a 330 or 320, but the 320 had a HP MMU as far as I remember, so 330 is more plausible.

>Is it possible to install a harddrive to this model or does
>it always has to be bootet over a network ?
You can connect HP-IB drives ( good chances that you have a fast HP-IB board installed along with a DMA board ) or try to find the legendary DIO-I 
SCSI board that may ( or may nor ) have existed somewhere in this universe... if you have a fast HP-IB controller then try to find a disk for it, if not then 
stick to net booting since the built-in HP-IB controller is slow ( 30-100KB/s or so, the fast one does up to 1.2MB/s... )
Make sure you have a BootPROM more recent than Rev. A in order to boot via ethernet.

good luck
Michael