Don't own one, but have shot them (not an H&R) and seen them at comps. Hyphanated also posted on attending a meet lately. He can also state what was prevalent at that meet.
300-500 yds isn't long range for this type of gun. 600 to 1000 is more common place. Most common are the Sharps and Winchester types. Black Powder Rules this class. Slow, big bullets (cast lead) No Jacketed.
Looking at the H&R the barrel is of sufficient length (32"). The breakOpen action I would have some doubts about. Also the sights are all wrong for a target application. You want a tang such as the Creedmore. Also the H&R barrel is of medium weight, might want to go a little heavier.
Now not saying you wont have fun with it. Competiave.....at what level...that's the question. H&Rs are priced at what us average guys can easily afford. I would say if you can get it to shoot 6" groups at 600 yds. with your handloads/black powder/cast bullets you have something to work with.
Here is a link to see what a mid-range Sharps type will run you. Not the best in the world and not the worst either.
http://www.cherrys.com/ped_cart.htm