Frankston Heights is a good place to rent, close to the Uni and Hospital. There are shops at Towerhill which is a short walk away, as someone else said there is a free shuttle bus service to Clayton. I don't live at Clayton, but know there are quite a few student accommodation places too.
In other words Monash Clayton versus Monash Peninsula (Frankston)?
Frankston is a cheaper suburb. It's campus is however much smaller as well as class sizes as Clayton attracts more students.
Clayton is better for clubs and societies and uni events in general.
There's an intercampus shuttle bus that is free for Monash students.
Really depends on where you are studying? Frankston is quite far from most places, while Clayton is much closer (although still not central). My preference would be for Clayton, but again depends on where you are studying.