Keep Perfect catches and useful Elite copies as your main candidates for training. Before releasing anything with a lower rating, check whether you still need it for your current team or Homeland.
Common and Good Potential
Common and Good are the lower Potential tiers, so they are usually the first duplicates to consider replacing when you find a stronger copy of the same Aniimo.

Avoid spreading scarce upgrade materials across several lower-potential copies. If you want to use a particular creature for the long term, keep looking for an Elite or Perfect version.
However, you do not need to remove a useful team member immediately. Keep the copy helping you progress until you have a suitable replacement, and check Homeland abilities and traits before deciding that a catch has no value.
Elite Potential
Elite is a good choice for an Aniimo you actively want to use. You can build around one while continuing to look for Perfect, rather than leaving your team underprepared during the search.

Focus on Elite copies that fill a role you need or that you enjoy playing. Finding an Elite does not mean you have to train it if it will sit unused in storage.
Perfect Potential
Perfect is the highest Potential rating and the main target when choosing a copy for long-term investment.

Keep these catches, then decide which ones deserve your materials based on your team. A Perfect rating makes an Aniimo worth reviewing, but it does not mean you need to level every Perfect creature you own.
Favourite the catches you want to protect before sorting through the rest of your storage. This also helps you keep track of promising replacements as your collection grows.
The Aniimo Sparkelf event offers a Prismana Sparkelf Egg with guaranteed Perfect Potential, giving you a specific reward to work towards.