Q:

Under which circumstances could a planet have two visible suns?

In the story I'm making, it is important that there are two suns in the sky, going at different rythms (maybe the planet orbits one of them each year, and the other each four years, for instance), and the planet rotates, making it so that in regular patterns, let's say in the beginning of the cycle, both suns seem "together", from the planet, like one is eclipsing the other, but as times goes on, in the mid-day (considering the planet which is rotated yearly as reference), the other sun seems to lag behind, until at exactly half the cycle, just as one of the suns is exactly at mid-day position in one side of the planet, the other sun is also at mid-day position, but in the opposite side of the planet.
One thing I thought, which I don't know how possible it is, is that one of the suns is incredibly more massive than the other, and it's very far, so it's like the smaller sun orbits the big one, and the planet orbits the small one, just like earth orbits the sun, and the moon does the same with the earth. The planet I thought of is similar to earth in size (that can change, is not that important) and climate (that is important, I'd like seasons to feel similar and wildlife in general to be similar).
So that the sun that is close to the planet irradiates a similar ammount of light and heat to our sun, I think it may need to have a similar size, but, would the other sun need to be impossibly massive at that point, so that the small sun orbits it? I know technically both suns orbit each other and affect each other, but in order for the visible cycle I'm describing to happen, I think one would have to be more massive than the other, but I don't know if it would be so massive it would just not be a sun anymore, but would just collapse. If I make that sun smaller, would mean the small sun is even smaller, and the planet would have to be either smaller as well (but gravity would than be very different to earth, which I wouldn't like), or way closer to the small sun.
This is just one way I've thought about it, and I'm not married to that idea, my goal is to look for a way so that the cycle I describe is possible. Just to clarify, there is a magic system intended, but I want it to be completely independent from how this sun system works, if possible. I want it to be possible with the science we know, even if it's a very unlikely (but possible) scenario, so I'd like to avoid magic and science fiction altogether.

A:

I assume that you want the two suns to provide roughly equal amounts of heat and light to your planet.
Since there are two stars, your planet should receive about half the heat and light from each star as the Earth gets from our sun (Sol), or it would be far hotter.
Stars near solar mass have luminosities proportional to their mass to the fourth power. Hence, a star of 0.9 solar mass (spectra class G7) would have roughly two-thirds the luminosity of Sol, and in order to receive half the light and heat, the planet has to be at a distance of 1.15 AU. If we then assume that the larger star has two solar masses (spectral type A4), its luminosity is 16 times that of Sol, and to receive half the light and heat as we get from Sol, your planet needs to be at an average distance of 5.7 AU from this star, or a bit more than the distance between Sol and Jupiter. This may seem close, but your planet would only get about 1/16 the tidal force that the Earth gets from Sol, though a bit more when it is closest.
You can increase the distance by making the larger star bigger and farther away, if you like. Above two solar masses, luminosity is roughly 1.4 x (M/Msol)^3.5. A star of three solar masses (spectral type B8) hence has 65.5 times Sol's luminosity, and it would have to be 11.5 AU distant; a bit farther than the distance from Sol to Saturn.

