What is a good starter motorbike?

Depends a lot on what type of riding that '35 miles' is, as in any freeway/highway will not be welcome with a 125 and a 250 is even an iffy.

A bike like the Honda Rebel 250 is a nice comfortable light-weight bike for easy city-commuting and the Kawasaki Ninja 250/300 is a bit sportier type ride with a little more gusto but at a different riding angle.

Suggest you enroll in a MSF Basic Riders Course, well worth the time and there are saving advantages in the insurance area to pay back the cost of the course plus they provide a range of different styles of bikes for you to test ride so you'll have a better idea what to look for.

Another consideration may be a bigger scooter-style bike like a Lambretta 150.

Chris has a good answer.. Its hard to be more specific when it isn't clear where (country) you are and how big you are. It is best to start small,as too big can be dangerous. but there comes a point where too small can be a bit dangerous too. The Rebel 250 is a great bike ( we call it the Hardly") but if you are 289lbs, it can be a bit anemic.