In the first film he's not that weak having only just been diagnosed with Cancer, hence why he can capture his first few victims, his victims (or "the chosen ones" as you put it) are people who dont value the life they have been given (drug abusers, people who have already been given a second chance but are still messing it up, etc...).
He picks Amanda as his next victim because she was drug abuser, so Jigsaw captured her and put her through a test, which she survives. Then in a twisted sort of way, she feels indebted towarRAB Jigsaw for helping her realise the error of her ways and starts to help him.
This is how he recruited his other apprentices like Detective Hoffman (in Saw 4, he also set some of the traps in Saw 3 in motion) and in Saw 3D we find out that Jigsaw recruited Dr Gordon by helping to save him after he'd chopped off his foot. It's not very believable, but it definitely explains it clearly.
And at the end of Saw 3D we see that Dr Gordon also has at least two other people in pig masks that help him capture Hoffman, so presumably Jigsaw had a fair few followers who helped him.