I use that mack-daddy 5-blade Gillette Fusion with a natural oil based product called SHAVE SECRET ($4 @ walmart, lasts very long time).
Yea, I know.... the fusion blades are really expensive, but they last a really, really, really long time iIf you always clean that blade from behind. Since the fusion is an open back design, you can do that easily using this razor. I think the Mach 3 is the same way. I shave almost every day and get up to three months out of a single blade. So, it's not that big of a deal $$$ -wise.
What a lot of people tend to overlook is that metal is subject to water erosion, just like rocks in a stream that end up round over time... So, if you rinse your blades from the front, you are dulling your blades in a hurry. Granted, it's at a microscopic level, but it does make a huge difference if you're doing it every day.
The shave secret product is really cool, too. You need only 5 drops or so and a tiny bit of water (depending how thick your beard is) rather than the standard compliment of water and shave cream. It takes some getting used to the first couple of times because it looks like you're shaving dry... but it works super-good. And you use much less water.
My facial skin is also very sensitive and my facial hair is very thick and grows in many different directions. Shaving has been a constant challenge for me since I started. And I gotta say, that this particular combo of products gives me the CLOSEST SHAVE EVER!!!! And it's pretty quick too... the Shave Secret product does not make a huge mess like foamy creams do...
Wow, I can type a freakin' novel about any damn thing, eh?