The JDM/J-Spec cams will give you some sort of gain, but they won't support what you want for your goal. Bigger custom cams will make getting some numbers out a lot easier (spend a lot in that department, you have to spend less everywhere else....as opposed to cheaping out on the cams, and then having to spend masses of cash everywhere else to make cams that are not up to scratch work for you).
In answer to grinding making the cams smaller, yes, grinding does...but it changes the profile, and lowers the base circle. To compensate for the smaller base circle, you shim up to the new cams, which gives you the increased lift the new profile offers. Doing this, however, will likely put undue strain on the valve train, due to the increased weight being pushed down on the valve springs by the shims.
Best bet for cheapness is to get blanks from mazda, and have them ground. As for specs, go to a cam shop and discuss your requirements - they have DECADES of experience with cams, and will be able to offer you the best solution for your needs.