Marlins make a good entry level gun in caliber of your choice. They can be smithed into a competitive gun as well. The current world record for 10 round on target is held by a Marlin. 1.73 seconds IIRC.
The Henry currently being manufactured is not considered a good gun for SASS. It does not respond well to smoothing and has a reputation for jamming when run at "cowboy" speed.
The Original Henry and copies made by Uberti are acceptable but are very heavy and slow to operate. They have the advantage of gaining Style Points. For the newbies, style points are mythical numbers that in fact are good only for your own personal satisfaction.
As stated above the Uberti 1873 is considered the top dog right now but the price tag is a little painful. An 1892 from Steve's Gunz will run with any of them.
Come on out to a shoot. If you like the old single actions and like to see people having a good time, it just might be your game.
Peeps are acceptable as long as they are tang mounted. Barrel mounted peeps or ghost rings are not allowed.