I assume that your description "after that it just shows a black screen saying welvome to jazz jackrabbit version... and after that nothing" means: After the console output "Welcome to Jazz Jackrabbit. version 1.3 [...] 1110 Kb memory alloc= OK", this console output stays on screen forever, and only the cursor blinks and accepts no further input. The program never proceeds to the graphical intro.

Suggestion:
Run the GOG shortcut that offers Jazz/HH95/Setup/Quit. Select option 3 here to enter SETUP.EXE. Choose: English -> Select Sound Card -> Sound Blaster 16 -> Yes (to accept BLASTER settings) -> pick any quality -> Exit and Save. Then run Jazz like you normally would.

Reason:
I can reproduce your problem (console output stays on screen forever, program never enters graphical mode) when I wrongly configure Jazz to use Gravis Ultrasound via SETUP.EXE.

Background info:
SETUP.EXE sits in the main directory of every Jazz 1 game (GOG ships two Jazz games, Jazz 1.3 full version and Holiday Hare 95). You must run the SETUP.EXE of the right game. Option 3 on GOG's menu (that offers Jazz/HH95/Setup/Quit) should run the SETUP.EXE that belongs to Jazz 1.3. If everything else fails, it's always possible to run anything by hand: Run a vanilla Dosbox installation, then type (replace pathToYourJazz with the correct path to the Jazz 1 game in question):
mount c pathToYourJazz
c:
SETUP.EXE