First question: Which system are you using for the server? Linux or Windows?
For both it is quite easy to run a server with CS 5.2, but for Windows it is a bit tricky to make it available for internet players.
In general you need a Half-Life server with maximum version 1.0.1.6, because in HL 1.1 the complete network code was changed. CS 1.6 is based on the new network code already, so for CS Beta 5.2 you need an older HL version.