Start with Black Mesa Source mod, then play HL2.
There is a fine line between clever and stupid.
I'd do Black Mesa (HL1 remake) then play HL2 and then HL2 episodes.
Original HL1 is out-dated, but it's still a good solid game.
I got along fine without any half lifes before #2, I played ep1 & 2. I wish there was more but I'd be fine if it ended there.
No matter how much Black Mesa is better in terms of graphical improvements and slight design changes, the original Half Life is indeed, the ORIGINAL Half Life. THAT"S how the whole thing begun. That's why, 14 years later, we are still crying for the next Half Life game. So yeah, try the original first.