Blackberries and raspberries do best in that pH range, but they will live and do OK in a wide range of conditions. Don't stress too much about it right now. Now that you have them, your first priority is to get those roots in the ground before they dry out.
Don't let the roots dry out, before or after you plant them. They probably came packaged in a plastic bag, maybe wrapped in damp newspaper. That's not a bad way to keep them damp. It's also not a bad idea to soak the roots for a few hours before you plant them. This does not mean after you plant them to keep the ground soaked to the point you drown them. It just needs to be damp enough that they don't dry out. I watered mine when I planted them and never had to water again.
Adding organic material is probably a real good idea. Some soils are pretty rich in organic materials naturally, but almost all can be improved by adding more. The organic material does not have to be peat moss, but it will work. First, you need to turn the ground and get out any grass, grass roots, and weeds you can, say to a depth of about 6 inches. Then put a layer of peat moss, compost, or whatever you are using 2 to 3 inches thick and mix that in with the soil. Then plant your berries.
I'm guessing that you got roots with a plant stem. You can also just use roots with no plant attached, but I would not expect that is what you got. Plant them the same depth as they were growing, probably no more than two to three inches deep. You should be able to tell where that was by looking at the plant stem. The bark changes color and appearance.
How far apart to plant them? Four feet seems to be a bit wide, but it is not really. You can use two or three feet if you want. When they grow, they will send a lot of shoots up from the roots, maybe not the first year but definitely the second and forever more. Your task will soon be to keep them contained to the row you want them, not worrying about them being too far apart. I have a strip where mine can grow and I cut anything down that comes up outside that strip. In a very few years, they will fill in between the space whether it is two or four feet. You will soon have a hedge, whatever spacing you use.
When you add peat moss or any other organic material, you will temporarily change the pH of the soil, but over time the soil will return to its natural pH state. There are different ways to handle this. First, you need to know what the natural pH state of your soil is. You can use that meter if you want, but I'd really suggest you contact your county extension agent, in the phone book under county government, and talk to them about getting a soils test done. Here in Arkansas it is free. I don't know what it might cost for you. I just have to go by their office and pick up the kit, fill the container with dirt, then drop it off at their office. In a few weeks I get the results in the mail. Not only do you get the pH, you get a lot of good information about the nutrient content of your soil. That test will tell you what nutrients your soil already has plenty of and what you need to add. It is too late for this planting but I think that is really, really good information to have on hand for the future.
To change the pH of your soil, you can add sulfur to reduce the pH or lime to raise it. Not just any sulfur or lime. Talk to the folks at your gardening center to see what products they have specifically for this so you get the right thing. I can't tell you how much. That depends on your pH and how big an area you are treating. The effects do wear off over time so every few years you may need to retreat.
With blackberries and raspberries, don't over-obsess on pH. Unless you are way outside the preferred range, they will probably do pretty well. You can address the situation over time. You dont absolutely have to handle that today.
Good luck.
