lots of things to consider: your pH is naturally acidic and you have
shade, else moss would not thrive. I am assuming you want to grow grass
instead, and in my lawn (I have similar conditions) I put down much of
the wood ash from the wood stove to improve the pH. But in shade I try
to be reasonable, grass has no chance, and have slowly made large areas
covered with vinca, lily of the valley, woodruff, lamium of all
stripes, and aegopodium. I accent them with ferns, hostas, daylily,
bloodroot, solomon's seal and forsythia.
If you want to grow flowerbeds, and you have part shade, it depends on
how well drained your soil is. I have sandy soil, and tulips,
daffodils, asian lilies, dianthus and peonies grow very well indeed.