The reboot series BY FAR.

second and third series, love them both.

Hard to answer when I've only played 2013, but it was a great game, and in my opinion better than any of the uncharted games.

First 3 games of Tomb Raider are package of one of best games ever, similar could be said for Resident Evil 1-2-3 and Silent Hill 1-2-3.

Just as a disclaimer i haven't played the PS1-games in ages and never played anything beyond those until the reboot which i loved. Also loved Rise of the Tomb Raider so that is my answer

third series, tried the old ps1 games and its digital throw up in my eyes.

The first series by far. Still play 1-3 regularly.

The third series. Out of the first series only the first game has aged well.

Core Design's TRs, by far.
Legend, Anniversary, Underworld were quite good, if bit easier than Core's due to easier jumping.
"Lara Croft and The...." games are very fun coops.
I don't consider Reboot games to be TR at all, they are just named that for marketing purpose to ride on well known and established IP.

Second series was the only one I played to completion, so that one. While I'm at it: Legend > Anniversary > Underworld (Too glitchy, confusing level design and the story wans't that great).

I've tried playing the first Tomb Raider and found it to be too clunky, and TR 2013 bored me to tears since it was more of a survival/shooter game than a "tomb raiding" one.

I'm really interested in trying Angel of Darkness though since there are tons of fan mods/patches to fix the game and it looks playable now, that game has always caught my eye when looking at Tomb Raider games and I don't really know why.