Medicated vs non-medicated feed is a personal preferance. I personally don't use it, others do. I really don't think there is a right or wrong in that situation. Just as some people start them on wire, I don't do that either. The most important thing is to keep their area clean IMO.
I have chickens and turkeys, and have never heard of being able to tell if a turkey has blackhead by looking at a picture. If my turkeys have it, it isn't causing problems. Considering that it can be fatal to turkeys, I am going to go out on a limb and say that they don't have it.
If you have a building to keep them in and a heat lamp, they can be started outside in cooler temps. I started some in an uninsulated building when there was snow on the ground. You just have to make sure that there aren't any drafts, and after losing some of that bunch I can also say that an insulated roof would be good too, as well as an extra lamp. The reason that I lost some of them was because the heat lamp bulb shattered. Ccondensation built up on the roof while I was at work, and I am guessing that a drop of water fell just right, going through one of the vent holes in the top of the lamp fixture. I have also started chicken chicks in September and had them go through a North Dakota winter just fine. To me it seems that the faster you cut back on their heat, the faster they feather out.
In my experience, they really aren't that difficult to start. Keep them clean, warm, fed, and watered. If you want to for the first year, you can also get a few Broad Breasted types to keep along with your heritage birds. You could have a BB bird for Thanksgiving and keep the heritage birds until they are ready. I have never had a BB turkey dress out at the mammoth weights that some people get, but I also don't feed for maximum growth. I try to keep the weight gain on the slow side, and it seems to help keep them from getting the leg problems that BB turkeys are prone to get. I have a 1 1/2 year old BB Bronze hen that might dress out at 35 pounds or so, and she still gets around very well.
Above all else, take the time to enjoy your turkeys, and I have to warn you, they are HIGHLY addictive!