honestly HL1 is a better game than HL2, as much as i love source
that said, go ahead and play BM first; you won’t get the nostalgia or whatever playing it today
What many people here don’t seem to be taking in to consideration is that nobody is going to have nostalgia from a 14 year old game that they played for the first time yesterday. That just isn’t how it works. If he didn’t play the game in 1999 then loading it up today isn’t going to do anything to better his enjoyment of black mesa. In fact I think it could possibly hinder his enjoyment of the mod. Why not play black mesa and get your half life experience in the way that is fitting for someone brought up in today’s gaming world and then 14 years from now you will have that same magical nostalgia the rest of us have of the original. Hell is that not why this mod was started to begin with?
In my opinion, it is better to play Black Mesa first, because most of us played HL in the past and knew what it’s coming. But with you having not playing the game, you will be surprised more often instead of a few times 
Agreed, it doesn’t really matter which you play first.
Agreed. Half Life 1 was my first FP shooter in my entire life (literally) and it was a blast. I played it maybe…1 week before I played Black Mesa. They were both extremely fun.
Half Life 2 just annoyed me. Both the boat thingo and the go-kar looking machine just didn’t entertain me. Half way through the car scene I just went “screw it” and turned on god mode anytime I reached a location where I’d have to go against enemies. It was just boring.
Then again overall it was boring and didn’t capture me like HL1 did. Something about it, the graphics, the gameplay. It all felt different to me, and not necessarily in a good way.
I Played Black Mesa before HL1, problem is not Graphics (i play doom from time to time), i just can’t stick with it, the gameplay is the outdated thing, Black Mesa isn’t here just for Graphics, it is here for gameplay too.
Play BM first so you’ll get surprised then play HL to at least get a nostalgic feeling about BM and HL. (Reversed, huh?)
HL1 is masterpiece with old graphics. BMS is mod dedicated for that masterpiece. I myself never expected for BMS to be better than HL1 because I prefer gameplay over graphics.
However to me it looks like its opposite for OP and he prefers graphics as far more important than quality of gameplay.