Suzuki: cutting out, geo metro, lean condition

Question
I have a 2000 1.3 swift, always starts first time, but if i start from cold and attempt to go up a steepish hill it cuts out and is difficult to restart.

Answer
I don't have any experience with your car.  I do have a Geo Metro, which is a Swift body, but it is a throttle body injected 1.0 3cyl.
I suspect that you are experiencing a lean condition (not enough fuel).  Next time take a can of aerosol carb cleaner, and spray it into the intake  after it stalls.  If it starts readily, then the solution is to determine why it's too lean.  If it starts harder, then it's too rich.  The other problem could be an ignition problem, which is a little more difficult to troubleshoot.
scotty