This is my two cents on which browsers use the most memory from my experience.
1. Chrome definitely kills your memory and overall speeds of your PC, especially if you're playing a game as well with it open in the background.
2. Edge is okay at running quietly in the background, however its usability is really bad imo and i wouldn't use it if i didn't have too, its Explorer reskinned and a new name basically.
3. Firefox, or the latest version is definitely the best at utlizing and using the least amount of memory on your system, it's quick, easy to use as Chrome and has a lot of features. There have been plenty of times where I've come out of a game of CSGO and thought, "Oh, I had firefox running that entire time" and i didn't even notice because it didn't kill my fps one bit.
I'd use firefox if you could, it's a very good browser but Chrome would, admittedly be the best if it didn't eat memory for breakfast.
*Make sure you select a 'best answer' to make sure we aren't answering this for months to come, lol.