So the other day I was driving home in the rain, and noticed that when I touched the brake pedal even lightly, the wheels seemed to lock up, and the van lurched forward. As soon as I let up on the pedal it went away, but even in parking lots a day later at low speeds, it is still acting like I am stomping on the brakes when I just lightly touch the pedal. I am looking for some information on what kind of problem this may be, and if it would be possible to fix as a diy-er who has replaced brake pads, wheel bearings, stuff like that.

 

Your rear axle seals are leaking. Or maybe your brake wheel cylinders leaking brake fluid. Either or, the oil on the brake shoe makes the brakes grab like crazy, then as you drive you burn off the oil and the grabbing goes away. Try coasting when its doing it and press the emerg brake pedal. If it does it then yup its the rears. Pull the drums to see whats up.
Its not likely the front, as the discs don't grab as bad if a little oil gets on them. You would have to drive though a deep puddle to soad the front discs to get them to shudder a bit.
My money is on the rears.

 

It also can be cracked shoes in the back, and occasionally a collapsed brake cable.