The controls were really bad back then too but that ends up kind of being the point, settling up jumps was all the fun of this game, once you realize it is a grid based game and once you notice where the grids are and what the rules are with jumping between differently spaced squares in the environment it becomes really quite fun and some of the pizzles, mianly in the later stages of each game and particularly the ones in tomb raider 3 are fantastically designed, some of the best in gaming and they really don't make them like this anymore but, yeah, you're never going to be hopping around like a speed runner, I don't even get how those people can get the pace of the game going that smooth. I was surprised by how fast I fell off the remaster, I used to love these games and beating them felt like the biggest accomplishment after months of trial and error but hmm, they just don't hold up cause of the controls and there is no way they can modernise it without ruining the core basis of the platforming system, any slight alterations and it doesn't work, even the camera gets screwed up but it also becomes completely unfun so you have to take the pain to get the fun unfortunately. (Not to mention it'll make some jumps a LOT more difficult, especially jump where you have to grab onto the ledge of 4th square)
And YES. To answer your question, Tomb raider 1 is by far the easiest of the three, not just easier puzzles but all the platforming is as easy as it's going to get, some of the levels in the later games try to add in more detail like a jungle level in Tomb raider 3 early on for example that hides the grids too much and it becomes ten times more frustrating, not to mention the enemies get so hard you need luck and there are some points that WILL make you drop the game for a time if not give up, a claustrophobic dark water under water level in the second game for example that is so hard to navigate and causes such stress (Tomb raider 3 starts you in motion on a slipe to prove the point that this is going to be so much more difficult that the last 2 games and you will die again and again) that I would advice now, if you find Tomb raider 1 to be too much and you expect these games to get easier or beat then without rage then give up now. These are like Dark Souls if in Dark Souls the bosses had such diverse movesets that they have no readable patterns and you had to attack them in very specific ways to damage them.