I have a recipe in my River Cottage Preserves book for "Family 'Beena".
For each 1kg of blaccurrants, apples or hard fruit, add 600ml water. For 11kg plums or stone fruit, add 300ml water. For 1kg soft berries or rhubarb, add 100ml water. Brine slowly to the boil in a saucepan, mashing gently with a wooden sppon, until fruit is softened. Remove from the heat, let strain overnight through a scalded muslin or jellybag. Measure the resulting juice and for every 1 litre juice add 700g sugar. Heat gently to dissolve the sugar, then pour into warm, sterilised bottles and seal. this will keep for a few months unopened.
You could use shop-bought cordials, provided they are good quality. Ribena, Vimto, Polish raspberry/cherry syrups, or any good flavoured cordial will do. In most cases you'll need to boil the cordial for a few minutes to get rid of preservatives which will inhibit the yeast in your brew. A full-sugar cordial can be used to prime the cider, check the sugar content of the cordial and aim to be putting the equivalent of 4-5g sugar in each 500ml. A "no added sugar" could be used but won't fizz up the cider and will add artificial sweetness - sometimes this is a good thing if you like sweet cider, and you can add extra sugar to prime.
