Although you can run complex material set-ups to achieve something like concentric rings expanding from the center of a mesh (like on a plane), often it is easier and quicker to simply create a mesh and set-up the UVs in such a way that it can be accomplished much quicker with a node function.
Expanding concentric rings - use a half sphere UV mapped from top to bottom. The top vertices represent the center pole of the sphere, the bottom edges represent the outermost edges. In this way, you avoid the math and achieve the same output at a reduced shader cost. In this example you would reshape edge loops to be equidistant, to avoid the texture appearing to slow down when panning due to the UV map set-up.
Use Filter > Other > Offset to offset the image. Then you may use the spot healing brush (Alt + LMB to select source area of image) to correct tiling seams. Another method is to copy/paste the image into a 3x3 grid and then fix the tiling.
Save textures as either TARGA (.TGA) files in 24 bit depth or PNG files in 8 bit depth in order to preserve transparency and image channels. Make sure to set the file format to 8 bits per channel prior to saving if using PNG. Unreal Engine also supports full Photoshop (PSD) files, however due to size impact it is not recommended to use this in your final project.
RGB Channels Only
RGB + Alpha Channel
*Note: TGA supports a variety of compression formats or uncompressed. PNG is a lossless compression. TGA will always save a maximum of 8 bits/channel. So a TGA file with 24 bits/pixel has 24 bits total across the RGB channels, whereas a TGA file with 32 bits/pixel has 32 bits total (8 each) across each RGB+A channel.
Ultimately, the compression of the source file generally matters very little as long as it is lossless because all textures will be compressed into DXT/BC formats for GPU usage.
If you are not using an alpha channel in your texture, make sure to enable Compress Without Alpha. That way the fourth channel is ignored.
sRGB should be checked off for every non-albedo texture (Roughness, Metallic, Normal, and Specular). Refer to sRGB and Linear Screen Space.
For channel packed mask textures, make sure to set the texture's Compression Settings to "Masks (no sRGB). Similarly for normal maps set compression to Normal.
Compression Settings - Make sure Texture Sampler method matches compression setting.