NotOneOfUs: I'd like to expand on this, since I'm having pretty much the exact same issue as the OP.
Doing a clean install of the current GOG installer version (2.0.0.7), it seems that in the Direct3D graphic mode for Tomb Raider 1, the game, as the OP says, goes black and has a stuttering sound when you try to start a New Game or Lara's House. All I can do at this point is CAD it. Every other graphic mode forces me into a window when the intro movies after the Eidos one start playing and, when trying to skip them by pressing ESC, cause the game to crash with the error "ChoosePixelFormat() failed: Cannot find a suitable pixel format"
Viewing the Problem Details, I get this for all the graphic modes (except Direct3D):
DOSBox DOS Emulator has stopped working.
Problem signature:
Problem Event Name: APPCRASH
Application Name: DOSBox.exe
Application Version: 0.74.0.0
Application Timestamp: 50ae1439
Fault Module Name: glide2x.dll
Fault Module Version: 2.43.9.9
Fault Module Timestamp: 50a6f146
Exception Code: c0000005
Exception Offset: 00010f1a
OS Version: 6.1.7601.2.1.0.256.1
Locale ID: 1033
Additional Information 1: 0a9e
Additional Information 2: 0a9e372d3b4ad19135b953a78882e789
Additional Information 3: 0a9e
Additional Information 4: 0a9e372d3b4ad19135b953a78882e789
I should also note that Tomb Raider 1 does not have a Setup option in the start menu, only 2 and 3 do.
Furthermore, I've found that TR1 seems to function properly in the game's specific "safe mode". The only differences I can make out from that mode and normal with Direct3D is, in its safe mode, the graphic detail can be set to Low, Medium and High, while in Direct3D, there is Normal and Mipmapping - though, as stated before, the normal Direct3D mode crashes when trying to start a New Game or Lara's House.
Hope this helps in finding a resolution.
I found the graphics setup mode (thanks to the GOG reply to me above) :
Start -> All Programs -> GOG.com -> Tomb Raider 1+2+3 -> Tomb Raider 1 -> Graphic Mode Setup.
I got the game to launch in full screen mode with the intro video and all but I can't remember what I did - sorry that that's not much help, I shall have to start making notes in future !
I still do not have this game running as I would like it to, however. There are still black borders and I'm not even sure whether I have it running at the optimal resolution for my monitor (native resolution 1920*1080). I've been sidetracked in the meantime, however, and can't remember my settings. I would also like to achieve a few further things to make the experience nearly identical to my playthrough on the PS1 many years ago :
1. I'm not happy with the controls. I can set up a WSAD scheme and select e.g. key 1 for drawing my weapon and spacebar for jumping, but the game seems to reset some of these settings when I start the game up again, which is frustrating. Ideally I would prefer to use a PlaySation-type controller but I'm not sure how to do it.
2. In-game music. The PS1 version had these awesome pieces of music which would play (from the disc) at certain points in the game and added a lot to the atmosphere. I realise that there is an explanation as to how to incorporate the music in the TR forum but I'm afraid I just don't understand it, computer dunce that I am :(
3. Save crystals. I, for one, really liked the save crystals in the PS1 version as I think they made the game more challenging. I don't know whether it is possible to play the PC version with save crystals rather than being able to save anywhere ?
I have also downloaded Glidos but haven't bought it as I'm not sure whether or not it would help me to resolve all of the above issues.
Apologies to NotOneOfUs that my reply isn't much help. The Graphic Setup Mode SHOULD be there, however, and it has been possible for me to launch the game in fullscreen.