The only low cost digital camera that can use a remote control that I know of is the Pentax Optio S1.
It costs about $160 and can use an "optional" wireless (infrared) remote.
I don't know the price of the remote control.
..
I'm looking for a not expensive simple point and shoot digital camera with remote shutter (better wireless) capability?
What should I buy? Thanks.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic