The answer will come down to what is the content of the file you are using. If you are using shapes based off of vector artwork say a circle or a corporate logo, vector based files are always ideal because they can be infinitely scaled without resolution degradation. If you are working with an image, you need to work with a raster file like PNG.
As Luis points out, if you are using PDFs for vector art, make sure you have the resolution settings set appropriately.
If you are using a raster file (PNG,JPG,PSD, etc.) the general rule of thumb is to make the file the largest size you need for the maximum scale and nothing more. For example if you have a 4k image going into a 1080 project you could save it at 2k if you are not going to scale it more than 2x 1080 resolution. This will take less RAM and be faster to process. If you are going to scale it >2048x1920 you could leave it at 4K. If you are going to always have it scaled to 50% of the original, you could even resave as 1280x70, again to save ramp and reduce processing by scaling in the app.
The real answer is to use the appropriate format (raster vs. vector) based on the type of element. If you go raster, make sure you have a file that supports the largest scaling (>100%) required and you can optimize if it makes sense (image will be <100% original scale in most cases).