Hello,
As previously stated the texture sizes should be powers of two on the sides. These sizes are as follows: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 or 2048 pixels. The textures do not have to be square, i.e. width can be different from height.
Standard image formats are JPEG (Joint Photographic Experts Group) and PNG (Portable Network Graphics).
JPEG has a lossy compression which means it can lose image quality each time it is opened and edited in programs such as Photoshop, Gimp, Paint.Net, etc. Often it will give you a smaller file size but it not the best option for images with text or straight lines. JPEG is best for photographs. Many programs have options when saving JPEG files for the amount of compression to reduce the file size. A higher compression will result in a smaller file size but also a lower quality image. Transparency cannot be used with JPEG files.
The compression for PNG files is lossless. It will maintain it's quality when opened and edited and re-saved. This format is good for images with text, lots of detail, and high contrast. PNG files also support transparency. On the down side the PNG can, but not always, be larger in size.
Overall both work well for certain types of images. It may be best to play around with both formats to see which works best for you.
I hope this information helps.
Best,
Anhton