Ask HN: First client for web dev

I'm getting my first client (personal, non-business) for a custom project and I'm a bit unsure as of how to handle some things, and I would appreciate some tips, most economical.

When getting the domain, which will cost X$ per year as well as the hosting, should I register it in my name, and pay for it myself while charging the client? Or should I set it all up in his name, with all expenses going directly to him, while I take the fee for creating the site?

If option 1, should I charge per year?

I Appreciate any tips/advice. Thanks