Fallout

Chronologically the games are played in order, i.e. 1, 2, Tactics, 3, New Vegas, etc. You don't need to play them in any specific order to understand what's going on, but if you want to understand all of the references then playing them in order is the way to go.

As for the first two games (and Tactics) being dated, that's also in terms of gameplay. The difficulty curve is brutal, a lot of aspects of the game are obscured and almost deliberately obtuse, much of the difficulty is on the basis of "hope that RNG doesn't screw you and expect to reload saves frequently", and there are hundreds of ways to unknowingly put yourself into a situation where it is impossible to complete the game, not the least being picking the wrong mix of stats and/or perks. All that said though, both games are amazingly detailed and deep, so if you can get yourself over the difficulty hump both are great games.