110 AC to 12 DC with high Watt
Do the math.  12 V at 700 W means 60 A.  That's going to require a thick and expensive cable, and/or significant losses in the cable, and/or a short cable.

This is why winches of this power are 12 V only when they are for automobile systems where that's the only option.  At 110 V, it only takes 6.4 A to deliver 700 W.  That's much more manageable with common cables and with less loss.

If you want to be able to use this winch sometimes at home and sometimes with a car, then dedicating a 12 V car battery for it at home is one way to go.  You get a 12 V, or "12 V battery charger" power supply, and connect it to the battery.  The charger won't be able to keep up with the current demand of the winch when on, but it will charge the battery to catch up whenever the winch is off.

Let's say the charger can deliver 20 A.  That means the battery is being discharged by 40 A whenever the winch is running, then charged with 20 A as soon as the winch is shut off.  The battery should be able to run the winch for minutes at least while sourcing 40 A.  In the long run, you're not going to run the winch continuously, so this system will probably work well enough.

Another thing to consider is that even though the winch may be rated for 700 W, it's not going to draw all that except under full load.  When the winch isn't pulling with its full force, it isn't drawing the full 60 A from the battery either.

Also note that this 700 W is the continuous rating.  Electric motors draw a lot more current when starting or when stalled.  If the winch ever gets stalled, it will probably draw, or try to draw, more than 60 A.

You will have to decide for yourself whether a 12 V winch plus car battery plus charger is cheaper or otherwise better for you than a 120 VAC winch.  If you might want to use the winch with just a car, then the former is probably the better tradeoff.