To play as a CS client, use winex3. Install HL and the very lastest full patch or it won't run right. HL runs about 99% as well on my box as it ever did in Windows, and I get far better pings under Linux when playing Team Fortress. Once you get Half-Life up and running correctly, it should then be just a matter of installing CS.
To run HL go:
winex3 .transgaming/c_drive/SIERRA/Half-Life/hl -console -opengl
To run CS go:
winex3 -workdir ".transgaming/c_drive/SIERRA/Half-Life" hl.exe -console -nocdaudio -game cs -opengl