You need a weak base for an E1 reaction to occur. Steric hindrance isn't a problem with E2 reactions b/c protons are pretty easily pulled off. If you have a strong base, E2 is actually the reverse of your order of reactivity. 3 > 2 > 1. Your order of reactivity is correcti for SN2 reactions where steric hindrance is more of a problem. If your base can act as a nucleophile, it will more likely act as a nucleophile when site of attack is less sterically hindered. If more sterically hindered, then your base will act more as a base.
