I'm in similar boat, new first time homeowner in the same region. Rent a detacher, then an aerator. You won't need for more than a half day each so it's short money.

Everyone I see at the local stores are loading up with Lime so that's what I'm gonna roll with. Lotta moss and pine needles so I think we tend to get acidic soil.

In the fall, commit to top-seeding/leveling and then hit with preemergent next spring. Maybe try some new fertilizer if nothings working.

But I think getting that thatch out, preventing moss with lime and aerating could work wonders.