Awesome Coin - pretty rare in any grade. I'm not a pro but I will offer my opinion on grading. PCGS or NGC are the industry standards - you have join up with certain groups such as ANA (for NGS) or PCGS directly to submit coins. Otherwise you could submit the coin through your local coin shop who is probably a member of one or both.
Now the other question - is grading worth it? You can figure that it will cost around $60 to get the coin graded. It is a draped bust (both varieties of this coin are worth about the same) - it is not the ultra rare and valuable flowing hair dollar. My concern with getting the coin graded is that it is not going to grade very well. It may get an "authentic" grade meaning that it is a "real coin" but damaged so no numeric 1-70 number would be assigned. I suspect this may happen due to environmental damage, the rim ding near the "S" on the reverse, the "x-shaped" cut in the center of the eagle, and it could happen if the coin has ever been cleaned. If it got a grade it would perhaps be in the G4 to G6 range, but I am not a professional grader and it is tough to make an educated guess in pictures.
If it was me I would get it graded - just to confirm it is a legitimate coin. That would make it easier to sell if you decide to do so, and if he got a numerical grade that would be a bonus.