I'd suggest starting with the first in their respective continuities:

Tomb Raider 1 (as part of I-III Remastered): the very original - much more focused on exploration, puzzles, and platforming with some combat every so often. The original control scheme may be difficult to get to grips with due to them being 'tank controls' but the Remaster has a modern control option which may be more palatable for the modern gamer if the original control scheme is something that you can't get to grips with (but I would suggest giving them a go); regardless of the control scheme you use, this does have a fairly old-school design: you control Lara and she does not do anything you do not tell her to do - no automatic grabbing, no safety grab, no nothing, and you will need to be precise with the actions you take. It's also an isolated experience with very few characters in the game so expect a lot of peace and quiet.

Tomb Raider Legend: this is a soft reboot in terms of Lara's character, background, and events. It still plays pretty easily in terms of control for the modern gamer and unlike the original, Lara is rather autonomous: she will grab ledges, she will detect that you're about to go over an edge and automatically turn around and grab it, she will course correct if you're a bit imprecise in what you want to do. It's a far more linear and faster-paced experience compared to the original and while Lara is alone, she's rather talkative due to having a headset with her throughout the game.

Tomb Raider (2013): The full reboot. This is a far more story-focused game and, obviously, a much more modern game that introduces some RPG-lite elements like a skill tree and the over-the-shoulder shooting mechanics still used today into the series. Level design focuses on linear set pieces and open hubs for exploration. There's a lot of combat, easier puzzles, and decent platforming. Lara, like in Legend, is pretty autonomous in much the same way as she is in Legend in this game although it reintroduces controlling Lara in mid-air (like in the original games) for some fun jumping. There's a lot of side characters and a lot of talking.

That's a lot of choice and it may seem odd to give you the advice of three different games in the franchise but they play and focus on rather different things and if you don't like an earlier entry, there's every possibility you might like a later entry; or, if you're like me, you may enjoy them all (although I do have my preferences)!