Common Assault can only be dealt with at the magistrates� court. Criminal Damage is an �either way� offence which can be tried or sentenced either in the magistrates� court or the Crown Court. If you plead guilty to both charges the magistrates have the option of sending you to Crown Court for sentence on the Criminal Damage. (If they do so you will also be sentenced there for the assault). However, they would be most unlikely to do so unless there are serious aggravating features surrounding the offence.
As far as they are concerned the more serious of these two offences is the assault. Their �starting point� when considering sentence for a first time offender pleading not guilty is a Community Penalty. You will be given credit for your guilty plea and, depending on the circumstances of the offence, they may feel they can deal with both matters by way of a fine or a Conditional Discharge. If they consider a Community Penalty they will adjourn the case so that the probation service can prepare a report on you to help them arrive at an appropriate sentence.
Whatever the sentence you will also be liable to pay a contribution towards prosecution costs (probably about �60). If you are fined you will be liable to pay a Victim Surcharge (�15) and you may be ordered to pay compensation to your victim.