How big should I draw my player character when I choose to have full hd backgrounds in my game?
It really depends on the perspective and scaling you are using. Do you have any background drawn, even a sketch or a mockup? It helps if you scale your background to the target resolution, then play around with character scaling until it looks good. Then check the size in px and you can start drawing for real.
To figure it out if you have no idea and no graphics yet:
Find a game that looks roughly similar to how you want your game to look in terms of perspective and character size, take a screenshot with a character (as large as you think it will ever be), scale the image to 1920x1080 if necessary, and measure the character size.
I made my first game at 1920*1080, My new game I'm working on is 1280*720.
The reason is that nowadays, you can have great looking games at 640*360 or less on a 1920*1080 screen.
I create my character's animations at 400 pixels height.
Because you can set the character's scale when creating a walkable area.
It's always better to have a big image scaled down than the opossite, because maybe at one point you will have to sscale it up.
Also, AGS does a great job keeping the quality of your character images when you scale it up or down.
So, think bigger than what you need and manage it in the Walkable area settings.