Does it run ok when it has warmed up? If so probably the auto choke. Sound very much fuel related, could be the fuel pump as has been said. The workshop manuals are hard to come by but haynes manuals are fairly easy to come by but not all that much helpful.
Suzis are pretty simple to be fair you probably won't need one if you have worked on cars before. try cleaning out the carb and having a look at the choke to start with might just be caped in crap. Look at the parts of the choke and check that they are free and not rusted up or anything. Try the fuel filters they may have not been changed and become clogged. then finally have a look at the pump and if it looks wrecked change it.
otherwise take it to a nice local garage (NOT SUZUKI DEALER) and let them have a look its usually something quite simple.
Let me know how it goes...
Dave
