As for all those saying there's basically no difference between HL and HL:Source, there is one significant difference which is that the Source engine has sticky ladders. In some places in HL1 (notably climbing in elevator shafts), you'll be very glad of those sticky ladders. Too bad the rest of the game looks like ass in the Source engine, but that's because precisely zero effort went into the conversion on Valve's part. All in all though, I still recommend playing the original rather than HL:Source.

Black Mesa is absolutely fantastic, but don't play it before the original. It would make playing the original afterwards a painful experience.

I never said it was. But the OP is asking if he/she should go straight to Half Life 2... that IS a sequel!

Edit: I do agree it is pretty cool though why direct someone to an unfinished product if they can just play the ORIGINAL and classic Half Life.

Thanks everyone for all your help and responses :)!

The one thing I don't have to worry about is not having HL live up to the hype, as honestly I'd barely heard about it before (I've been out of the PC gaming scene since the early 1990's). One of the primary advantage that HL has for me is that it will actually run on my current system (a 2009 Mac), unlike many/most other more recent FPS!

I think I have decided to play the games in the following order:

Half-Life
Half-Life: Opposing Force
Half-Life: Blue Shift
Half-Life 2
Half-Life 2: Episode One
Half-Life 2: Episode Two

and then, if I feel like some more, Half-Life: Source, and finally Black Mesa (Black Mesa is windows-only, so I'd need to fiddle around with WINE/Wineskin to get it to run).

I'm well aware of that, but in that thread Blak Mesa is quickly discarded and the discussion veers into Half Life: Source vs the original.

Counter-intuitively, play Half-Source if you want to play Half-Life with its original art. For some reason, Valve decided to apply Gearbox'es High-Definition pack (from ~2001) to stock Half-life in one of the recent updates. I personally don't care for it. I think it does too much or not enough, leaving the art looking inconsistent. I ended up picking up original discs to play the version I wanted to play. :/

I haven't tried Steam Half-Life or Half-Life: Source for about 9 months so things may have changed.

You can disable the HD models in the Half-Life 1 engine games from the options menu.