No bucket carrying. (well, not if they are full. I will carry an empty bucket that has only the siphon in it)
a) Python/Lee's Ultimate Gravel Vac/DIY Waterbed fill kit.
b) Rubbermaid garbage can on wheels with a fountain pump.
You can use a) or b) for both dirty water (empty the tank) and clean (fill the tank), but I do it a bit differently.
I use a siphon into 5 gallon bucket to drain the tank, drain enough water into it so I can clean the filter media, and vacuum the floor of the tank, and turn on the fountain pump in the bucket, connected to a hose that goes outside, to empty the bucket as often as needed (several times for the larger tanks). I bought an extension cord that has an on/off button that I can step on to activate. I found it at Wal Mart, and tried it. I like it so well I now have about 3 of them (or is it 4?).
I refill the tank with water that I have previously set up in the Rubbermaid can. It has dechlor, any minerals or peat moss (depends on the tank) and whatever else is needed, and is the right temperature. The fountain pump with a bit of vinyl tubing lifts the water into the tank.
Rubbermaid Brutes come in several sizes, with lids and the castors are sold separately. They work great on lino or hardwood, not so great on carpet. Not too bad in a low, dense pile indoor/outdoor sort of carpet. Be careful rolling them around. The lid is not water tight, and will leak if the water sloshes. And it will. Better to get the larger can and not fill it more than about 3/4 full.
As for the work I do in cleaning the tank: I usually rotate jobs, so that one day might be filter cleaning, another day might be scraping the glass (with the siphon hovering close to remove the loosened algae) and another day might be to concentrate on a more thorough gravel vac. I do not actually plunge the siphon deep into the planting substrate, but on the 'more thorough' day I will work pretty hard at getting into all the corners and doing my best to clean under the decorations.
Volume of water change is almost never less than 25% and 50% is more common, partially because it just takes that much water change to to do the cleaning I want to do.