I'm like you OP, very much a skeptic, very much a non believer in anything ghosty. And then I had a ghost.
Had about 6 months where I kept seeing a figure out of the corner of my eye. I'd be sat on the sofa, and turn my head and he'd be stood in the doorway, or I'd be washing up and look up into the window and see the reflection of him stood behind me. Just long enough for me to jump out of my skin, and then he was gone
Also had a couple of occasions of thing moving. Would be upstairs and hear a noise, go down and find a spoon in the middle of the floor in the kitchen. Put it on the side and went back up. Hear noise, spoon back on floor. Repeat two more times.
It was only ever me who saw him, wife and daughter saw nothing, and the things moving only ever happened when I was home alone.
Lasted about 6 months, nothing in 10 years prior in the same house, and nothing in about 3 years after.
Looking back, I was going through a really rough time, my Mum was dying and work was being epically shit, risks of redundancy etc. I reckon it was just my mind playing tricks on me, stress makes you a bit loopy.
It might be the same for you. Moving house is stressful. You put the car seat down on the edge of the table, not really paying attention, and it falls off. You think "I'm sure I put that in the middle" and now you're on edge. Next door have the TV up loud and its the piano. Now you think somethings playing the piano in your house, even more on edge. And you get tenser and more stressed and your brain starts filling in blanks, until the move stress goes and you're settled in your house and you start relaxing, and so the "ghost" dissapears.
Or you really have got a ghost and he's decided he likes you, so he's stopped pissing about.
On a related note, I've been listening to "The Battersea Poltergeist" on BBC Sounds. Worth a listen if you like a bit of Woo