Showing categories in front-page

I’m not an expert by any means but I would suggest using:

[gallery category="animals"]
Or with term_id:
[gallery category="14"]

Using the [gallery] shortcode on the page several times should not cause any issues.

Only problem with this is that there is no limit so the better option would be to either select the ids (if known):

[gallery ids="1,2,5,7,9"]

or use the gui to add the images and use the category filter to limit the items.

Unless you want to create a specific function that does has a limit on the initial query.

Hope this helps.