Which are the best texture file formats to import to UE4?

I also use TGA and PSD. I used to use PNG- call me a bit of a PNG fanboy if you will, mainly from my legs in the web and graphic design field. However, there has been buzz lately that PNG is going the way of the dodo, with the trend being moving over to vector formats (mainly SVG) on the web. I’ve always been a raster sort of guy, so this hurts my soul a little… it is what it is. But that’s the web and such…

I prefer TGA for ease-of-use across the board; as KVogler pointed out, from a raw code point, it’s pretty painless to work with. TGA is also very widely supported. PNG is great because it is a lossless format (and thus generally free from compression artifacts, like JPEG), but its original intended use was as a replacement for the GIF format. Portable Network Graphics vs Graphics Interchange Format. While PNG can be used for rendering (both offline and realtime), that wasn’t the intended use, keep that in mind. TGA however, has a slightly different history. Per Wikipedia:

… The format can store image data with 8, 15, 16, 24, or 32 bits of precision per pixel – the maximum 24 bits of RGB and an extra 8-bit alpha channel. Color data can be color-mapped, or in direct color or truecolor format. Image data may be stored raw, or optionally, a lossless RLE compression similar to PackBits can be employed. This type of compression performs poorly for typical photographic images, but works acceptably well for simpler images, such as icons, cartoons and line drawings.

For rendering “stuffs”, I personally jump on the TGA wagon, since it strikes a chord as far as being more intended for that sort of stuff. In the end though, it comes down to what works best for a given person/project. Your toolchain, art style, target package size, etc all come into play here. Someone mentioned that UE handles compression internally as it pleased; don’t be mistaken: there are size differences between the formats, even after UE waves its magic wand over them. So be sure to do your own tests and find what works best for you, quality/size/performance wise.