If we are discussing this from the perspective of doing the brand mascot
I would tackle it as a two-fold process:
1. Mascot design, which will involve the character design process
You will need to start with formalizing the brand characteristics that have to be infused into the mascot. This will also help with the animation.
This can be handled with many techniques. My preferred two: word list (list 30 words that describe the brand and desired look and feel that should go into the mascot design) and mood boards (a collage design that combines inspiring imagery and gives a good gut feeling of what the mascot design should communicate). https://en.wikipedia.org/wiki/Mood_board
This will help you create a compound of brand identity connotations that will serve as a guidelines for the design.
Next, do the mascot design itself. It may already be done, but in case it is your task, these are the resources I find useful:
Best app mascot designs http://mashable.com/2010/06/07/best-mascots/#pEGgaO7omkqa
Hootsuite mascot design process http://lauraeagin.com/designing-an-app-mascot
Character Design inspiration Pinterest board https://www.pinterest.com/explore/character-design/
As opposed to the animated video character designs (like Pixar characters), mascots are generally kept minimalistic, cartoonish, simple and cute.
Cuteness is a huge factor that should never be underestimated.
Animal mascots are the most popular technic (and it is a whole anthropologic issue in it's own right and deserves a separate discussion ;-).
2. Mascot animation
There are two great resources I have found fascinating:
The choreography of animation for UX designers, an article written by an UX designer in collaboration of one of the Disney father founders. https://medium.com/@becca_u/the-principles-of-ux-choreography-69c91c2cbc2a
And the "Illusion of life", the video about 12 main animation principles that explains how animation works and what makes us recognize the emotions in the movement. https://vimeo.com/93206523/
If we are discussing this from the perspective of doing just the UI animation, like the Android video you have shown in the other question
All of the above still applies, with two caveats: the items you will animate will not be an anthropomorphic objects (but they sure can be, think the Pixar Lamp), and the animations will be simpler. But the principles are the same. What you need to transmit is the character, so treat the elements like they are alive and reacting.
Which elements of UI typically need to be animated, from the top of my head:
- Those that need to attract users' attention: tour guide indicators,
- Those that move the user or UI from some state to
another: transitions, loaders, change of status indicators, etc.
- Those that gamify the experience: badges, points, achievements, hats,
Since your app is an e-commerce, there is plenty of UI elements you could animate in both fun and down-to-business way (I would steer clear of sensualism, it's very subjective and can drive a part of TA off): loaders, purchase state indicators, badges, notifications, gifts etc.
Commerce as a topic has plenty of symbolic material to work with. For instance, carts and shopping baskets that bounce happily when user hits "Purchase", credit cards that slide through the terminal, a loader that could look as a present that unwraps itself, a shopping bag that happily goes green to show the eco standard of the app, a gift certificate bouncing for a few seconds in the ancillary panel, flying parcel for the shipment progress bar. And so on and so on.