I've done the backpack for a brief period and didn't like it. Too hot and the weight on the back got to me after awhile. Then I got the Topeak Beam rack and used that for a few years of off and on commuting. But this rack is limited in what you can carry. With all that you need to haul, I would suggest getting a dedicated rack and panniers.
I am now using a rack and pannier system and really like it. I would suggest getting a rack that has a dedicated second rail for hanging the pannier on. This way I can have a trunk bag on top of the rack and the second rails on the rack make it easier to add and removing the panniers. The rack I have is the RackTime ADDIt, and you can find it at lots of places like this: http://www.therandonneeshop.com/products/show/61-addit
Whatever rack you get, make sure that it has side rails to keep the panniers from swinging into your back wheel.
The rack and trunk bag works well as you can put your computer and clothes in the pannier and lunch and small stuff in a bag in your trunk bag. Then when you get to work, just remove the pannier from the bike and carry it like a brief case or messenger bag. Then grab the bag from the trunk and off you go.
I used to have showers and lockers at work, so cleanup wasn't an issue. Just go laid off, so we will see what happens at my next job. But the more you can keep things at work like shoes, belts, ties whatever, the easier. You could do the baby wipe cleanup in the restroom. They make some that are larger (Like 8"x11"😉 and do not have perfumes. I'll see if I can find a link for some of these, but a quick search should show up easily.
Finally, the more you can reduce to haul around the better. Could us just use thumb drives and bring work home that way instead of the computer all the time? Also, you could drive in one day a week and bring a clean set week's worth of clothes and then take home the laundry too. Thus you don't have to haul clothes everyday.