Advice for care of this tree. Second picture is before

Moved into this house in September and so became owner of this apple tree at the bottom of the garden.

We managed to get rid of a lot of the ivy at the lower level and cut the ivy off from the root so a lot of what’s remaining is dying off and falling out. You can see some of what we chopped off stacked up by the fence!

We don’t have the budget to have the tree professionally pruned, so came here hoping people might have some advice for anything we can do ourselves? A lot of the lower branches have greyish coloured lichens growing along the entire length, is it best to try and remove as much of these branches as we can? The very top of the tree will obviously be unreachable but will try my best with the rest!