Moving up to a Baron

Most ambitious plan, grasshopper...

Insurance co.'s are concerned with total time and multi time especially
when insuring a pilot in a hot twin like a Baron. Any multi time
whether HP or not is good, although a pilot with a new multi rating
would probably have to fly X number of hours dual in the Baron before
solo. Probably the best course would be (I think someone else mentioned
this) to get the IFR rating (the CPL wouldn't hurt either) and build HP
complex time if possible, then get the multi rating. Once you have that
you could fly right seat w/Dad and log that time as PIC.