Car insurance is expensive and yes you will be classed as new drivers. The DMV is hell and they take joy in making life difficult for anyone who walks through their doors.
I would avoid East Brunswick because you will end up driving north on the parkway to get to work. It is bumper to bumper from 7-10am and returning home the parkway is solid from 3-7pm. In addition, you want to avoid tolls which quickly add up. If you are in East Brunswick you will have a toll if you take the turnpike.
Somerville and Piscataway are not 30-40 min commute but more like an hour plus during the morning commute. Traffic in these parts is slow. Google maps will give you estimates but always increase them by 15% if in the metro area.
For areas to avoid - Wayne, Cranford and Little Falls are always flooding so they are best avoided. Montclair is very mixed so if it seems too good to be true then it is and avoid it. I would avoid areas such as Roselle, Rahway, East Orange, Orange, Elizabeth, Newark, Hillside, Union, Springfield (too mixed for my liking) and most of Jersey City (parts by the waterfront are lovely).
I am in South Orange which is ok and the town next to me, Maplewood, is also ok but you need to be in the part of town further away from Newark. Since Newark laid off policemen there has been an increase in the spill over of crime into our town and Maplewood.
The advantage of Westfield, South Orange, Millburn and Maplewood is that you don't need two cars. All have good transportations links, supermarkets, pharmacies and doctors (including paediatricians, obns etc) within walking distance. Millburn and Westfield have very nice town centers with coffee shops, a good library and little cutsie shops to wonder around.