Definitely look into ride share/carpooling. Maybe once you start you'll find you have a coworker in your area willing to carpool, alternating who drives, or just letting you pay them to ride without having to drive.
How long is the commute by car? If it's 20 minutes by car, but an hour and a half by train/bus, that's a big difference to consider, especially when you figure it each way.
I had a commute of 45 miles (40 minutes) each way for 12 years. In the beginning, I drove myself, then I carpooled, then we used a van and had a bigger pool, then I went back to driving myself (no bus/train option). Each option has its pros and cons, but now that I have a four mile drive to work (ten minutes door to door), I never want to commute again!
One other thing to look into--are there any ways to discount the transit expenses? Are there company perks (they pay for part of the pass)? Does your city/state provide vouchers or supplements to take public transportation (some do in order to encourage people not to drive, in order to reduce congestion)?
As for car insurance, whether you have full coverage or liability only may make a huge difference in cost, or it might not. You have to get quotes for the specific driver and vehicle from different companies to know for sure what that will cost you. If you go with liability only, you need to know you can recoup from the loss yourself (I've had liability + uninsured motorists only for years, no point in full coverage for the cars I drive.)