what would be the best way to remove some rusting in barrel ? what should i soak it with? what works the best ?

I always remove the barrel from the stock, then spray the insides with Birchwood Casey Solvent. After it soaks in for a while I spray once more and then start running a brush down it. After I have done that for a while I like to run a few patches through with the same solvent. Then some dry patches.

If it is real bad, I break out the JB Bore paste and use that. Normally that will make the barrel shine again. Granted it will not do anything for pitting, but it will pull the rust out of the pits.