The first thing a lighting desgner has to know is what is being lit.
How big is the set?
Is it an "open" stage or a proscenium?
Does it have to troupe or is it to be a stationary show?
What kinds of puppets are being lit? Marionettes? Hand puppets? Others? Combinations?
Will it be performed in a room that can be darkened, or is there to be a lot of ambient light?
Then one has to know about the show to be lit.
Is it a comedy? A drama? Are there day scenes/night scenes?
Do different areas of the stage need to be lit independently of other areas?
Because of the many questions, it is impossible to give a simple answer to your question. You can piece together a simple but effective lighting system entirely from items from your local hardware store, as long as the needs of the show are met.
The specifics of more sophisticated lighting would determine which lighting instruments would be required, how many of each type, and consequently what king of controller would be needed to operate them.
Also the positioning and hanging of the lights needs to be addressed. Will the lights be hin on trees or a truss out front? Do any need to be hung on battens above the stage itself?
Really you can go so many ways. You could spend about $150 up to about $5,000. The more you can tell us, the more accurately we can advise.