Security is tight anywhere you go in DC. No matter it's a government building, museum, or gallery, airport-level security is mandatory.
If you can, don't wear clothing or shoes with metal parts. I had a metal buckle on my belt, and wound up having to 'unbelt' myself in every building. Haha, I didn't know so many people want to see me undress.
Luggage and bags:
back-pack. Be prepared to have it searched each time you enter into a federal building. No big deal.
Clothing/Shoes/Weather Gear: comfortable shoes. Theres a lot of ground to cover.
Photo Equipment: like all other trips get your supplies from your home area. If you try to buy in the gift shops they will charge you out the wazoo.
Luggage and bags:
I don't necessarily think that there is a 'best type' of bag to take, since that primarily is a personal issue, though I would say that when I travel I try to not look too much like a tourist (the typical ugly American comes to mind) though it is something that is generally easy to find out.
Base what you bring on where you are going and the climate at that particular time (this is common sense, and probably not something that I would have to tell anyone).
Clothing/Shoes/Weather Gear: Washington, climate-wise, is pretty temperate. The summers can be a bit humid (thought if you have been anywhere in New England during Summer or Winter you probably won't notice) but comfortable. The winters are relatively mild (there is a temperature drop, but, at least in the past few years, there has been little snow.
There are lots of trees so Washington is particularly beautiful in the Fall and there are the Cherry Blossoms that bloom in the Spring to look forward to.
Toiletries and Medical Supplies: Shouldn't be a problem. The good thing about traveling to developed countries are that such things can almost be taken for granted (thought if your medical needs require a pharmacy (our version of a 'drugist' or a 'chemist'.) many can be found with minimal effort.
During the Spring and Summer months, particularly if you have a problem with allergies, Washington can be particularly difficult. Pollen counts can be extremely high, so if you're taking something like Claritn or Zoloft I would definitely make sure that my supplies were current, since (at least in the United States) such drugs are not available over the counter, and require a doctor's prescription.).
Photo Equipment: Shouldn't be a problem. If you primarily use a digital camera, I think that it may be relevant if the camera is USB or SCSI, or if you require a Flashcard reader because, while I have seen a few internet cafes around Washington, I haven't actually visited one.
Camping/Beach/Outdoor Gear: I'll add to this when I get more information:-)
Miscellaneous: More pictures forthcoming!!!!!!!!!!!!!!!!!!!!!!!!!!!
Luggage and bags: Security check points like bag checks and metal detectors will slow down your entry to most museums. To help this process along try not to bring large bags, etc.