...even though I haven't played a single game in either of their respective franchises, and it doesn't look like I will anytime soon. Not to mention I haven't seen much of either game, though I really like what I've seen. And my currently playthrough of Resident Evil 4 makes me want to play the Tomb Raider reboot. That was especially true when I was in rusty underground areas in RE4.
No I haven't. I have extremely vague plans for playing through Uncharted 1 and 2 at the end of the year to go with the Metal Gear Solid HD collection (I don't like playing two games in the same series back-to-back, but alternating between two franchises makes me feel really good somehow. Last summer I played through Super Mario Galaxy 2, Metroid Prime, Super Mario World, Super Metroid, Super Mario 64, and Metroid: Other M all in a row, for instance).
And in all honesty, if I ever get the Tomb Raider reboot I'd want it to be my first Tomb Raider game. As for Infinite, I'd want to play BioShock 1 first, but I don't care about the sequel.