I suppose it will be very different for each child.
Most new borns will like looking at high contrasting toys/pictures. I know April used to stare intently at her black and white book from very very early on.
Around 6/7 weeks they will start to follow high contrast toys/mobiles with their eyes.
Most babies start to hit out at things around 8 weeks or so. We started putting April on he baby gym then and she began flailing her arms around and hitting things - by 10 weeks she could intentionally reach for something almost accurately and put it in her mouth. (Best to have small toys with easy to grag loops or rings)
From about this time onwards they begin to get more and more interested in reaching and grabbing and investigating toys and rattles....(and anything else within their grasp!!!)