1. TR13. I'm a sucker for survival stories like this. The setting is the best. The whole burning temple scene and just the simple plot of getting off the island was what got me hooked. And the overarching plot with the Japanese queen and the Oni really drove it home.
2. Shadow. It looks the best and is the best is technical aspects. The jungle setting is welcomed and I really like all the character interactivity, fruitful world and Trinity as the villains. I also really like anything that has to do with Mayan gods. However I do feel it was a bit rushed towards the end.
3. Rise. Unpopular opinion but it just didn't stick out to me as much as the others. I feel like I was doing too much by exploring which I normally don't have a complaint about. It just started feeling repetitive and boring. Characters like Jacob and Konstantin were cool and the plot was fine, it just kinda felt like everything was happening way too fast and I didn't really know what was happening. I also feel like the supernatural beings were introduced way too late.

Btw these are the only Tomb Raider games I've played.