SOP is to get the autopilot in at 1,000'AAL, but manual flying is permitted - subject to common sense issues like RT loading and PNF's workload. I'll hand fly the odd departure or arrival every now and then, more so if there's a sim coming up. Some captains are keener on hand flying than others, so it all depends on who you are with and conditions on the day.
As for an autothrottle - in my dreams . . .