I say go for it. There is no better place to start; don't worry about playing the original Half-Life their releasing a complete remake of it on the source engine {the HL2 engine, and I'm not talking about the HL:Source port} called Half-Life: Black Mesa.
Black Mesa (game mod) - Wikipedia, the free encyclopedia
Once that’s finished it should hold up well in today’s standards because the game is still great, just dated graphically, but the core elements are there, so what there going to do is update the graphics and add more enemy models. It should be legendary.
The only think you need to know about HL2 is that your Gordon Freeman a scientist that was there during the inception of the alien invasion. Your there to bring order.