Hi I do the exact same commute. It's really easy when it works, 2 or 3 stops on the 40 min train. You can buy a termly ticket that makes it about 50% cheaper too (only avail to students), the monthly pass (avail to anyone) knocks about 1/3 off the price compared to paying for tickets per journey.
Obviously you need to think about what happens when the trains are cancelled (snow, floods, engineering, etc), what's your plan b? If you can drive and have access to a car, you will be eligible for a parking permit (you live more than 10 miles from uni), parking with a permit is £3 per day. There are obviously downsides to driving into/out of the centre of Birmingham at peak times.
Without a car as plan b, what happens? Lectures are recorded but so is your attendance is recorded and if it falls below a certain point,there are issues, so you need to be attendin as much as poss. The odd transport issue will be expected and forgiven but you will need a plan b.