I also use the stock battery. Have for 5 years now. When I pull line I only do 20 feet or so at a time and then let the winch rest an leave the motor running for the battery. That said... My battery is now looking completely shot. Mostly from vibration I'm sure. It's never let me down but it's to the point now where I'm worried it won't start. Looks like its time for a yellow.

 

Yellow top and run wires under the grill under air box and there's drilled 2 holes in plastic plate 2" in fro t of battery...put positive in 1 hole put negative in other and the mounted perfect to side mounts....

If you use your winch a lot on long pulls then definently look to deep cycle at some point the optima yellow top is an great battery closed cell so no real venting can be mounted in multiple angles and has good cold cranking amps for starting...
Used to link 6 for my old shop van (had a audio store) and took em LOW and back up a lot.

Short runs etc a normal battery is more than fine as long as its not old and ready to retire the plates will degrade after time.... that's all batteries not 1 in particular so if you have a good battery go have fun...

With either battery I'd recommend leaving the jeep running it charges while running. If you do a big pull you risk running the battery low enough that you won't have the initial power needed for the starter.

 

I have ran a winch on my factory JK battery for the last 3 years... 120k mile rig. I routed my winch control into the cab, and keep the engine at 1,500 when winching... IDK what the fancy programers allow you to set idle at for winching, but I think 1,500 and free is a good target.

 

I think keeping the winch pulls shorter under heavy loads is more important than upgrading the battery... A dead battery is allot more convenient then a fried winch. I just killed my motor pulling out a pair of ingrates duallys for free.