Converting avi files to newer format

I have a lot of old (2003 up to 2009) family movies with .avi extensions. I have read the community responses that avi's are "old wrappers." (Not techy myself; just copying terminology I've seen). My goal is to change these into whatever files will allow me to do both of the following 1) watch the movies on my MacBook Air (2020 version running Sonoma 14.2.1) and 2) hopefully upload these new files to Photos and then ultimately to the cloud.

I see that using Handbrake is a common solution, but then I read that "converting" can affect the quality of the file (either video or audio track.) Will Handbrake automatically "convert" these to H.264/H.265 video and mp4 audio files (which I have read is what you want) and therefore I don't have to worry about loss of quality?

What software do you recommend I use (is Handbrake the best or are they all pretty much the same?) Is using Handbrake pretty self explanatory? Once Handbrake "converts" these files, is it creating new files that I then have to import back into Photos? Once I am able to get them into Photos, am I "safe" -meaning the new format will be stored in the cloud and I will be able to view these in the future?