Can a worn drive-train be upgraded incrementally or should it be all at once?
It really depends on how worn out the drivetrain is. The best way to check this is by checking your chain with a chain gauge. If the gauge reads under 1.0 you might be alright with just changing the chain out. If it reads 1.0 or higher (ie the guage at its max reading easily fits onto your chain or even has some play) you probably have a toasted drivetrain.  That is not always the case - sometimes I'm surprised by how worn out a drivetrain can appear yet still be improved with a new chain. On the flipside, which is the more common side, if you have a chain that reads completely worn out chances are the rest of your drivetrain has worn with it and replacing the chain will only make things worse. You'll know pretty quickly if this is the case and if it is you'll to start replacing other components:


Replace your chainrings if you chain jumps or chainsucks in the front. Sometimes you can get away with just replacing middle and/or small chainrings as the largest chainring tends nto to wear out as quickly. 
Replace your cassette if your chain jumps in the rear or shifts very poorly or both. With newer cassettes there is no option of chainging individual cogs. It's all or nothing.



If you don't own a chain gauge or you're unsure as to what components need to be replaced, find a good mechanic to inspect it for you. They should be able to diagnose your issues and suggest replacement parts as needed.