What kind of water heater should I get for the bathroom?

It's according to what type of power you have. I researched all on the market when thinking about one. I had propane tank so I went with that type. Check your local gas provider, they most always have the top-rated one. As for size they are compact in size but can really cut back on the electric, plus any size usually cover a entire home.

Do you have gas? Then a tankless is great. If not, an electric tankless requires a very substantial electric upgrade. For electric, a small tank would be more efficient and easier to install.

If you are only heating water for this sink, make sure the flow rate of the tankless matches the flow rate of your faucet or you will never get hot water. If you need this for other faucets and a shower, then be sure it has enough output for multiple faucets used at the same time.

Regarding flow rate, a tankless will not start heating water with just a trickle unless it has a recirculating pump to keep a small amount of water hot at all times.

For a shower, it's really nice to have a temperature control for the water heater right next to the shower. You set the water heater to your ideal shower temp and then only turn on hot water for showers.

In addition to the excellent advice from Jeri here is a page from Amazon with tankless water heaters made for bathrooms.

https://www.amazon.com/s?k=bathroom+tankless+water+heater&crid=1KK99CA5346KU&sprefix=Bathroom+tankl%2Caps%2C486&ref=nb_sb_ss_i_1_14

i got some good answers. now i have to figure out which way to go. thanks

You will most likely need an electrician to install. My boss tried it and didn't have a great experience on the small bathroom size. Hopefully they have advanced since then.

Gas or electric? I have never seen a tankless system installed under the basin. Where do you live Nick? Local building codes determine placement.