I would recommend a Slim or Fatboy adjustable; you'll have total control. And probably start with an Astra Superior Platinum blade. From there the combinations are endless.
If I had to recommend a specific razor for sensitive skin it would be the Standard Razor but before I'd recommend spending money I would certainly agree with the previous posters about varying your technique and prep regimen.
I am going to +1 on the Microtouch one. Or the Van Der Hagen razor, which is the exact same thing. They are cheap and generally available locally. They are mild and efficient, easy to get the hang of, and I feel that they are every bit as good as a vintage Gillette Super Speed... which is quite good. It will allow you to get your feet wet and see if this kind of shaving is for you- without breaking the bank. If you like it, you can upgrade piece by piece. The VDH razor is what got me back into wet shaving after not doing it for about 15 years. I started with the razor kit. It comes with blades, so I just used it with canned foam. After a couple days, I went and got a cheap brush and soap. Then nicer soap. Then a nicer brush. Then a nicer razor... and so on. repeat as needed. As far as technique, I only did with the grain for the first month. Then started going with and across the grain after that. After a month of that, then I started going with, across, against. You say you have very dense facial hair, so you might not be able to get away with a just with the grain shave. But doing with /across can be incredibly effective. Especially moving from a cartridge to a double edge. Good luck! I have never been able to shave with a multi blade cart. It always made my face feel like it was set on fire, and I would get terrible ingrown hairs from electric. Until I got back into wet shaving, I made the decision that not shaving was better than miserably shaving. So I just used a beard trimmer to cut the scruff as close as possible. Getting back to traditional wet shaving has been great. I have never felt so good, or had healthier, happier skin. You have made the right first step. I hope it works out for you.
One thing also is make sure you know the grain of your beard. With with grain on the bottom of my neck is 180 from the rest of my beard. So as Tom said one of the "hundreds of things" the choice of the razor is not going to help. I got joy from reading a person describe a razor as "beginner". it is plenty aggressive for me. I to have weeper ready skin and I must be very careful of pressure and direction of strokes.
I also have very sensitive facial skin. Preshave oil has helped me previously. There is not so much need for it now as my general shaving technique has improved. Any vegetable oil will do, but adding a bit of tea tree oil is not a bad idea if you are not allergic. - Splash water on your face - Put 4-5 drops of oil in your palms - Massage it into your beard - Shave as you usually do PS: I have not read the entire thread, but I am sure a lot of people have said this: Going against the grain is very hard on the skin. Instead, shave across the grain twice - that is far more gentle to your face.
Echoing what's said above. I'm sold on vintage but occasionally use the Proglide with perfect results every time...BUT I would never go ATG from the start if I had dense hair as you describe. That's most likely what's causing your difficulty.
Count me as another sensitive skin face shaver. I had considerable rash and bleeding early on as I was trying out new DE razors and blade combinations. Once I found a complimentary combination of blade & razor, plus as my technique improved, the irritation subsided and bleeding was a rarer occurrence. I also was a generous user of pre-shave oils and creams, and post-shave soothing balms. Both these prep and post-shave applications did wonders for my irritated skin. I will occasionally still get some slight post-shave rash on the throat using a DE razor (ironically, I get absolutely no irritation from SR shaving), but the DE razors I use are on the aggressive side. NO ATG passes.
I agree with Tom about the razor situation which can cause an endless search for razors. So the real issue become development of techinque in terms of skin preparation, lather generation, razor handling, and post shave activities. Now in my signature line the discussion of 30 Day Rule and Focus covers the technique development phase. For a mild razor, get a Gillette Tech or 1950s/60s Super Speed razor. For lather find a good brush and cream to start with. A good Generaton 3 synthetic brush and C.O. Bigelow / Proraso is one example of an easy lather maker that can allow for cushion and slickness (there are others as well). That covers the shaving end of the spectrum. The one thing that is over looked by many is pre and post shave as a way to immediately improve your shaves while you are developing your technique. 1. You should have a good after shave balm. Nivea and Dove for men are two examples. You should use this twice a day while you are learning. One time at the opposite end of the day from the shave. If you shave in the morning, then use the after shave balm in the evening before going to bed. That will allow for more hydration and skin healing. 2. Always get your skin completely moist for at least 5 minutes before shaving. A shower before shaving is a great way to do this. 3. After your shave use the after shave balm again to provide more healing and moisture. When you move over to Traditional Shaving methods and develop your technique you may find that you can let go of the evening (opposite to shave) balm application. I hope this helps give you some food for thought.
I also agree with the Gillette tech. If you have a Body Shop nearby I would go and get some Macca Root shave cream from them and find a sampler pack of blades to try out. I switched from multi blade cartridges back in August and haven't regretted the switch one bit. DE blades are a fraction of the price and work so much better. I would also suggest checking out all the tutorials that are available on YouTube. Mantic59 is a good one to check out. Best of luck to you.
I know you are thinking of a Micro Touch but if you want something a little more substantial look for a good Tech or Super Speed.