What kind of grout/caulk is best for tiles in a bathroom ?

Usually a silicone caulk, and look for it to say for kitchens and baths. Grout is different, and will depend on your tile joints, etc. Here is some basic info: https://www.diynetwork.com/how-to/skills-and-know-how/masonry-and-tiling/grouting-tile

A link is attached for how to choose grout type for your tile. Good luck

https://www.builddirect.com/learning-center/flooring/choose-grout-ceramic-tile-facts/

For finishing tile work, I like to use grout that has latex in it. It smooths out and is it's own sealer. Rule of thumb is to used sanded grout in a space between tiles that is 1/8" or wider. Otherwise, use un-sanded grout. For caulk, use one specifically designed for kitchens and bathrooms. They now come in a variety of colors. Good luck.