It only looks weird to do planks at the office for a little while, then people get used to it 
FWIW, I finally bit the bullet last fall and committed to consistent core work My routine takes only about 10 minutes 3 times a week and if I am pressed for time, I can still get some benefits from just 5 minutes. The silver lining to having a super weak core is it does not take much to make improvements! It really has helped my back, both on and off the bike.
I feel the biggest benefit came from doing dead lifts. I was inspired to do dead lifts by the TR video and was quickly sold - best bank for the buck exercise known to man.