Just bought a used rv from private seller

As with most things RV related - it depends. Does the tank have FW in it? If so, how long has it been in there? I have never sanitized our FW tank but I have only ever owned new RVs and empty every time I return on a trip. Public water is treated and chlorinated and we don't drink the water from our FW tank. On a used RV I would probably sanitize it once before using. Simply drain it (there should be a low point drain for your FW tank), add about a 1 cup of bleach to the inlet/fill (easier if it's gravity fill - if not, add the half a cup to the end of the hose before hooking up and turning the water on). Fill the FW tank, turn the water pump on, cycle some water through the lines and out each faucet (sink, bathroom, toilet, shower, outside shower), turn the water pump off, let sit for 24 hours and then drain the system. 

Would I need to rinse the system?

yes I would definatly add sanitizer and flush the system out.  fille with the sanatizer and let sit overnight then drill, fill again and drain again.  its a small amount of work to ensure the tank is clean as you never know what kind of water the people before you put in it.  a lot of people don't use their fresh warer tank for drinking so they put water from anywhere in it.  if you intend to use it for drinking water like I do then for your own piece of mind I would clean it.  I don't like using bleach anymore as you hasve to rince it for days, it seems, to get the taste out.  I found THIS .  yes it costs more than a jug of bleach, but allI did was put a bit of water in the tank, premixed this and added the proper amount then filled the tank up, ran water to all the faucets, toiler and hotwater heater to make sure the treated water was everywhere then topped up the tank and let it sit over night, drianed it filled with fresh, flushed the lines and drianed.  best product I have found yet.