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.