Simplified Rules
The rules of Dungeons and Kittens are a stack of small mechanisms that build on one another. There is no need to use everything from the very first game: it is perfectly fine to start with the bare minimum, then enrich the game session after session.
Step 1: the bare minimum
Only abilities and Heart points are used. To succeed at an action, you always roll three dice and a single success is enough, whatever the difficulty. Everything else is ignored.
Step 2: triples
Add the rule of triples: three identical dice always trigger a small bonus, success or not. It is immediately visible on the dice and easy to explain.
Step 3: re-rolls
Introduce re-rolls, tied to Purr-ecious items and Cattributes. This is also a good time to present the concept of childhood.
Step 4: the rest
Add difficulty levels, skills with advantages and disadvantages, then Furr-endship points.
Meowgic and Catfights rest on all of these mechanics. For the first spells or the first Catfight, it is better to take the time to explain clearly what is happening rather than apply everything at once.