I'm sorry to hear that it is likely that you have MS. Getting such a diagnosis is always scary, and MS can be very uncertain.
Have you done any reading over at the National MS Society website? You can find it at www.nmss.org
As for starting Avonex...there is lots of evidence that suggests that the earlier you start any of the disease-modifying drugs, the better your chances of reducing the disability that MS can bring. They all are designed to at least slow the progression of the disease, and reduce the number and intensity of exacerbations.
Note, though, that they won't stop ALL disease progression, nor stop all exacerbations...but, speaking from personal experience, here, if you can reduce even by one, the number and intensity of flares you experience, you'll be much better off than those of us who didn't have such medicines when we were first diagnosed...
Bottom line: if he's willing to prescribe it, I'd certainly start Avonex, and continue to explore the other drugs, in case there is some reason in the future that you want or need to switch.
Don't hesitate to ask questions about the lp, if you have them. Good luck with it next Friday.