You will need a 2 5/16" ball. Make sure it is rated high enough for the trailer weight.
I just installed the dual-cam parts of the Strait-Line hitch on my Classic. Impressive piece of equipment. I use 1000# bars on my Classic with a hitch weight of 870#.
Yes, the 800# bars should be plenty heavy enough for you. Better the bars be just a tad too light than bars way too heavy.
John W. Irwin
2005 Classic 28 "Sabre-Dog III"
2013 Silverado 2500HD Duramax/Allison LTZ
WBCCI #9632, TAC TX-10