Use normal granulated but also some Certo (liquid pectin sold at all major supermarkets). I appreciate that you were hoping not to have to go out to the shops, but when I do Strawberry Jam I let the strawberries rest in sugar overnight before boiling them up. You could nip out later for the Certo.
About 1 medium Apple per pound of sugar should do it. Ideally cut the apple into wedges, core, skin and all, and sift out the bits at the end (the core and skin have most pectin in) Sour apples are higher in pectin than sweet ones.
My top tip for set strawberry jam is to steep the berries in the sugar overnight, cut them in half at least and then mix them into the sugar, squeeze over the juice of a lemon and then tip the whole lot into the pan next day
Heat gently to dissolve the sugar in the juice and carry on until you get a set.