I would suggest some preparatory (and useful) homework to build some skills.
I would suggest decorations for an infant’s bedroom.
You can pick any cartoon, but this one of Mikey Mouse offers enough trials to get you going (and will make a wonderful gift to new parents).
Make the face and ears as one piece from 3/4” thick MDF.
Choose a template material (1/4” or 1/2” MDF will work fine).
Make it large—maybe 12” to 18” across.
Nothing in the drawing is round. So you will have to use some proportional dividers to get the right shape.
Intermission: More to come.
The video shows how to use the proportional dividers. I got mine from Amazon (plastic ones) for about $10.00. I’m sure that the brass ones in the video are more expensive.
After you have drawn the shape onto the template, cut it out with a jig saw or band saw. Use a sanding block to smooth out the contours.
Attach the template to the 3/4” MDF and trace around it. Remove the template.
Cut to shape using your saw, then re-attach the template and use your router or router table to get the 3/4” stock to exact size and shape.
Make a second template for the painting pattern. That can be made from anything you have in your shop—preferably something in the 1/8” to 1/4” thickness.
Your router bit will not reach into the crevices where the ears attach to the face. You can use your saw to get in there and sand paper to smooth it out, or a hand saw (pull saws work great) or attach some sandpaper to thin material and use that. In any case, you cannot count on the router to get into small spaces. You will have to use your imagination to come up with solutions for that (or post a question here, if that comes up).
Use a round-over bit on the edges of the face.
Use Sealcoat or shellac based primer (B-I-N) as water based paints and primers will “raise the grain” and make the surface look like rough sandpaper.
Don’t fool yourself into thinking that this will end up being a one-off. Make it nice enough and it will be in demand for every parents’ new nursery.
The painting template is simply for tracing the design onto the mouses face. I would freehand the paint job. Corrections are easy by painting over the errors.
A simple project like this, will give you the template making skills, the template cutting skills, and the drafting skills to make most projects.
If Mickey Mouse does not suit you, there are tons of other cartoons. Some will be difficult as they are drawn in three dimensions, but most are adaptable.
Note: I would make a hard pass on including the background. Let the parents just hang the piece on the wall. The bigger you make this, the easier it will be to produce. The 12” to 18” is a good size range, but larger would be more impressive and easier to cut (with a jigsaw). Too big may be problematic for finding wall space. I like French cleats for mounting on the wall.