I don't know if I can help you. I do just about every single thing the opposite of what others recommend.
1) You should start with real juice from a real orchard, not from concentrate, no preservatives. Why? It tastes better, and it will ferment easier as any preservatives in the commercial juice will tend to hurt your yeast.
2) I would not add any sugar. Why? Personal preference mostly, but you can get a great 6-7% ABV cider from the juice all by itself, so there's little need to turn it into more of a strong wine-like beverage unless that's what you want. It sounds like not. So don't add any sugar, none at all.
3) I've never used the English cider yeast but based on reviews of others, it's not that great. I like the dry Cote des Blancs or US-05 the best, they turn out appley in flavor, whereas other yeasts tend to turn out very dry and bland.
4) I don't use yeast nutrients, I don't find them necessary. However if you are using pasteurized juice of questionable source, it can't hurt.
5) I don't use Campden. I actually pasteurize my cider at about 160 F for 15 minutes. I have had far more consistent and tasty results this way.
6) Pectic enzyme is not necessary. If your cider will not clear after fermentation, use gelatin instead, which works better and can be withheld if not needed.
7) I'd plan on racking that cider about once per week for the first 4-5 weeks at least. This will reduce the amount of yeast in the cider and slow down fermentation, which will allow your cider to retain some sweetness. Otherwise it is likely to ferment very dry, specific gravity below 1.000 and often as low as 0.992-0.994. If you just leave the cider in primary the whole time, you're most likely going to get a very dry cider unless you kill with Campden and sorbate. I have not been very successful with killing yeast with Campden and sorbate. I have found I get a more stable and sweeter cider from racking often over the course of several months, not days or weeks.
8 ) Carbonation should be a crapshoot. If you ferment in a hurry, you will likely get a well carbonated cider that is also bone-dry and winey as the yeast will keep on working in the bottles and eat up all the remaining sugar unless you pasteurize. You can try that, although the one time I pasteurized my finished cider, it ended up tasting like cooked applesauce and I didn't enjoy it as much afterwards. In my opinion you really need to ferment to dryness, then wait another month or so just to make sure it's done-done, and then prime and bottle. In this case, most of the yeast will fall asleep or die so then carbonation should be a crapshoot. The more carbonation you end up with, the drier the cider will be. I like mine a little sweet, so I actually prefer it to be still or petillant (barely carbonated) and get disappointed when it carbonates heavily. The longer I wait before bottling, the more likely it is that my cider will be sweeter and not heavily carbonated. If I wanted carbonation AND sweetness, that's luck. I've only experienced that one time out of about a dozen batches. It CAN happen, but... it probably won't. Crapshoot.
In conclusion, low and slow is the way to go, and keep it simple. I like to ferment in the 50s for at least a couple of months. No need for extra sugars or odd chemicals, except gelatin. Gelatin is your friend. If fermentation ever goes too fast, hit it with gelatin and knock 90% of the yeast out of there overnight. Then your cider will stay sweeter without having to add a bunch of chemicals or backsweetening. When specific gravity is around 1.015-1.020, I like to hit with gelatin with a goal of ending fermentation for good at around 1.010. This results in a nicely balanced sweet/tart cider that isn't so dang dry. Anything below that will become more and more dry and tart.
By the way... your homemade cider is not going to taste like Woodchuck or Angry Orchard or Redd's. It just won't. Real cider just does not taste like that! But if you follow most or all of my guidance above, it will likely taste even BETTER than those commercial versions.
My 2 cents. You can make cider the way you've described, and it might even turn out great. I just wouldn't do it that way. So like I said, don't know if I've helped. But perhaps given you a few things to consider, for future batches if nothing else. Experiment and do things your own way, that's the best way to learn.