Honestly, I never put a thought into this. Now that I’m texturing, I’m considering file formats. The only consideration I ever made was alpha, so I always used pngs for most files.
Can someone recommend a good file format to use as a standard. Or a good reason for better workflow?
I am using Gimp for texturing or using Blender to do texture painting. What do you guys recommend to save files at.
Also, if you have input on resolution any pointers on that would be great.
Depends on what you need.
png is lossless compression, but bigger file size (if your images are not single-color, of course 
)
jpg is lossy compression, so you lose details/gain noise, but get smaller files.
tga is lossless as well.
Games often use formats such as dds because of hardware support to decompress them (yes, OpenGL has support for that too).
As for resolution, it all depends on your detail size, on how big your models will be on screen, on how detailed you want to get different parts. There is no rule of thumb really