I usually rinse them out as well. I do have the Medela quick wipes, but for some reason they seem so chemical-y to me!
I would say that after each pumping session it's a good idea to transfer the EBM into storage bags (I also love Lansinoh) because if you will be freezing the EBM, you should only do so in increments of 2-6 oz and that's normally one pumping session.
Good Luck, it gets to be a habbit and before long you'll be used to it, so will your co-workers. Today a partner (man about 65) wanted to meet with me but asked with sinceraty, "Do you want to pump first?" Weird! But Funny.