If sunlight was red then the red sun would be long living allowing evolution to progress longer on that planet. That sun would have been born before our own sun as well, so if compared to the current Earth Date then an Earth-like planet could easily have life that's been around way longer and maybe more advanced. If sunlight was red the sky most likely wouldn't be blue. Problems involving gravity would put a livable planet farther away from the star which creates its own problems. The reduced energy from a bluer spectra would probably not provide the necessary amount to support life which raises issues if we consider the sun to not be a contributing factor of the redness. Our red light would follow a black body curve centered on red, so the plants and animals wanting to reflect the light would be cyan or blue, and would blend towards white as they reflect more and more sunlight. Ones wanting to absorb the light would be red and blend more towards black as they absorb more and more light. Green always has a more efficient alternative so there would be no pressure for green and probably very little of it, if it appeared at all, Colors as viewed by the natives would probably be viewed in shades of red due to the lack of other color components in the sunlight. Similarly the rainbow would be red-shifted.
A red sun could be cooler than our own and last much longer allowing life to evolve to higher levels. Solar heating would decrease faster with distance so the net effect would be that the sun would appear much larger in the sky (probably at least twice as large). The decreased strength of sunlight would place limits on the food chain. Less species in a web means more specialization and less burden. Less input energy means less plant growth per unit area. Less growth means slower metabolisms, tricks to find food, and longer lives have selective pressures. Low metabolism, slow-paced (culturally), long-lived, intelligent creatures would be selected by evolution (k-selection). Note that intelligence would be more likely to develop.
Vision would be adapted for red. This means the natives would most likely see in shades of red with maybe some yellow mixed in for shades of orange. Likely their visible spectrum would be shifted to see infrared and so heat would be visible to you average creature. This may help accelerate intelligence or hinder it on caloric, etc. If it was useful to distinguish between plants and animals that might use the other colors they could end up with a visible light range similar to ours, plus heat vision.
The increased likelihood of predator and prey both having heat vision results in typical camouflage adoptions not being very effective. You might see more fauna with thick fur and similar features, to insulate their heat signature.