If you are inexperienced using AE and have little or no experience as an illustrator expect to spend two or three months getting this project to look the way you think it should look. There is no magic button.
To do this kind of animation and After Effects you will need to separate your artwork into layers so you can animate the hands and arms moving, and the legs. You may even need to create illustrations with the body parts in different locations. This takes a fair amount of time to learn how to do right.
If we could see your original artwork we could give you better pointers, but this is a fairly long and complicated process for almost all animations.
A cartoon style animation of a character walking into a scene and tightening a nut then smiling then a logo popping up that lasts 10 seconds could easily cost you $1000 if you hired an experienced animator with all the right skills.
If you are very experienced and talented in character animation and you have a real good understanding of how to use the software this 10 second animation could easily take you to full workdays.
You could separate the character from the background and then use puppet pan to make his arms and legs wiggle a bit, but that's about it. If you want to make him smile and have him twist the wrench and tighten a nut you will need a lot more drawings. If you want him to walk into the scene you will need even more drawings.
One more thing. After effects makes videos and videos for a company logos on websites is a really bad idea.
To make an animated logo using this style of a character for your website you could either create an animated gif (Quite possible using AE and Photoshop) or by using Adobe's new flash replacement Animate.