Making stuff look good depends on several things:
- Programming: Making interesting shaders
- Art direction: Making sure the colors blend well together, that different elements stand out without sticking out like sore thumbs, and basically designing the objects that have to be modeled and textured
- 3D art: Making the models look good while optimizing the UV maps and without using too many polygons, bones, etc, and giving the models interesting and characteristic animations.
- 2D art: Making decent textures and baking some visual effects that would be too expensive or impossible to draw in-engine
Overall, I'd say you could do something that looks good using only shaders, but that'd probably require shooting for a simpler aesthetic, while making good stuff and using the default shaders could result in the game looking too same-y compared to other Unity projects.
Edit: Preferably, I would like a simple looking, colorful/cartoony quality to the visuals.
I'd say it applies more to having a single central theme as the base from which everything is built from, and that you
do have to take care not to fill your game with mechanics, but I think that applies more to mechanics that clash with the main theme or take too long to develop, draining the team's enthusiasm in the meantime.
You could make a good an interesting game simply by creating a tightly-packed experience where everything works towards transmitting the feelings/experience/message you intend it to, even if you didn't have an amazing main mechanic; but yeah, it's simpler to build games based on a single, good mechanic.