Child's Highchair = Where to begin?

Hello! I'm relatively new to restoration - my father has done quite a bit of furniture himself and I've learned a bit from him.

My first project is a child's highchair that was my husband's grandmothers. It's over 100 years old and I would like to restore it as a Mother's Day surprise for my mother-in-law.

The chair is in suprisingly great condition, considering it's been in a garage for 20+ years. Just a little wobbly...

Where do I begin? Should I strip the old finish off (and using what?). Should I take apart the chair first and do this in pieces, then reassemble? It has all of the original hardware (screws, etc.) What can I use to better secure the screws after replacing?

Any suggestions would be greatly appreciated! My dad is on a month long trip to Australia with my mom and I can't use him as a resource right now!