I'd skip classic HL and go with Black Mesa. I grew up playing a lot of Half-Life, CS, TF, and that disk game. Black Mesa is a fantastic true to origin update. It pairs better with the HL2 story than the original game, as the original had story elements left out. You do not need to play one before the other, it just helps with the story depth if you'd like.
Blue and Opposing forces are also very fun, so if you do go the classic route, add those to your list before HL2. Again, not needed but adds more depth to the story if you are curious.