The razor blade model is a killer. They sell the handles at a loss in those starter packs knowing you'll buy the blades.
If in a hurry I shave in the shower. My taps are mounted on a chrome plate that acts as a mirror.
However for best results I wash face first (or straight out the shower), rinse face with water as hot as I can, then apply shaving gel and rinse hands. Then run hot water as hot as I can to rinse the blade in. Rinse face in water as hot as I can stand, then with water as cold as possible, dry then moisturise.
Not sure it makes a difference but always feels best, that and I saw it on a beauty TV programme and all.
IME changing blades before they go blunt is the most important thing.
I find that the hot vs cold water thing is that for me, hot water works best as it rinses the blade more thoroughly (I think) so has less hairs stuck to it ergo less snagging.