Get a hands-free pumping bra.
This is a bizarre contraption (as if pumping isn't bizarre enough), but if you are pumping regularly, it is wonderfully liberating as it allows you to multitask while you pump. There are multiple types, but the one that I found most convenient and secure was basically a strapless bustier with 2 holes to put the breast shields into (Simple Wishes Hands-Free Breastpump Bra, Pink, XS/S/M). This was especially great when I went back to work because I could just keep it in my pump bag and use it over an unbuttoned shirt and whatever nursing bra I was already wearing.
If you end up having to pump frequently for any length of time, buy enough pump sets to get you through the day without having to wash them.
This way you can put them in the dishwasher and clean them all at once. The last thing that you are going to want to do when you are pumping 6-8 times a day is hand wash pump pieces, and all the constant washing can add up to a significant amount of lost sleep.