Both Black Mesa and Half-Life 2 run on the Source engine.
Which one you should choose depends entirely on what your goals for your project are. Black Mesa's version of Source is heavily updated from Half-Life 2, but the development tools (Hammer, Model viewer, Faceposer etc.) are largely unchanged. If you're just making an extension to the Half-Life universe taking place in Black Mesa using the same weapons and enemies, I'd say Black Mesa is an excellent game to base your mod for.
If you want to make a full total conversion mod with new weapons, NPCs and functionalities, you're probably better off starting from scratch with Half-Life 2, or rather Source SDK 2013. However, from your description, this sounds a little higher level than what you're looking for, so I'd say use Black Mesa.