Here food for thought: I recently had all the same questions choosing a winch...
My 99TJ weighs in at approx 3800lbs, as mentioned before take your jeeps weight and X by 2 =8000lb winch is ideal. That'll get you out of pretty much any jam. The reason for a winch that's good for double the weight, is simply when you or someone else are stuck in a mud pit, on a hill, etc, is that physics adds more pull to your line.
Your stock alternator is plenty good, I had a 880CC Amp battery and upgraded to a 1300CC amp, just for shits and giggles.
You can most defiantly bolt a winch plate to your stock bumper, use a good grade bolt though! Don't want that to be falling off when you need it most...
I bought a smittybuilt XRC8000lb winch, cost was $680 Canadian $, it is a little slow with line speed, but when your stuck it gets the job done and then some! You can buy a pulley (aka "snatch block") and that will come close to double your pulling power, but take care when using it, your jeep tjs frame is only good for 10,000lbs of pull.
Best of luck, hope this was able to help you out, and as always when winching take proper caution !