What would you guys recommend to use for greasing the headset bearing?

My bike is 10 yrs old and the headset was never serviced. I felt couple times and the head piece is lose. I took it apart and notice the grease became white powder alike. So I think I need to put some new grease in it.

Automotive, or marine bearing grease is fine, or you could spend more and get a bike specific grease from your lbs.

Marine Bearing Grease is the standard reply, its the cheapest and comes in many sizes

A tube of Park grease is only, like, $7 if I recall correctly. It'll be good for all of your bearing grease needs on your bike. Just make sure the bearing races aren't pitted at all. A lot of times that happens if a bike is ridden with a loose headset. If your wheels haven't been serviced in a while either, it might be a good idea to go ahead and do the hubs while you're at it and Park grease is good for those too.

Greetings
+ 1 and for sure you need new bearings, trash the worn caged ones and replace with loose bearings and plenty of grease. Don't forget to reuse the seals.
Regards