How big of a winch do I need?

I've been looking at winches because I tend to go wheeling by myself. The only thing I've gotten stuck in so far was some really deep, wet snow... and I think I was high centered by some ice. So, I don't need a huge, frame curling winch. I just want something that could pull the jeep out of some small situations. What is the smallest rating that I could get away with? Do I need one with an 8000lb. rating? thanks!

I just read someplace that you should multiply your gross vehicle weight by 1.5 to get the minimum pulling force for a winch. Does this sound right?

I just read someplace that you should multiply your gross vehicle weight by 1.5 to get the minimum pulling force for a winch. Does this sound right?

This is true but stating it in terms of gross vehicle weight is a little misleading. the Jeep has an official GVWR, this has nothing to do with winch size recommendations. The minimum winch pull rating should be 1.5 times the weight of your vehicle and the maximum cargo you will be carrying. Generally minimum winch pull rating for a Jeep is 6000lbs. That gives you 4000lbs for the Jeep and cargo. If you modify your Jeep or carry tools or lots of camping gear, you will quickly exceed 4000lbs, that moves you up to the next winch size, 8000lbs.
Not many people would recommend that you go off roading alone but if you do, your winch is now your 4X4 buddy that you depend on to get you out of tough spots. Just like your human buddies, make sure the winch is dependable. Dont skimp on it or your asking for frustration. What if you got stuck and your human buddy just stood there and refused to help you, you would be pissed. Same thing with a winch.
Ive got an 8000 Warn on my Jeep and personally, I wouldnt go smaller or cheaper.

Yeah I always go overkill on anything I buy, and consequently, none of my tools/ parts have let me down. Id say get the best one you can afford. (Ex. I bought an 8,000lb jack for my Civic lol)

Oh, another point. A winch isnt a toy. Its probably the most dangerous piece of equipment on the trail. Make sure you use it safely, ALWAYS, not just sometimes.
And a winch is only as good as its accessories. This means dont forget to pack shackles, tree savers and snatch blocks, the more the merrier. Also make sure your tow points are up to winching. The winch and cable is only as good (and safe) as the point its anchored to.
Sorry to go off topic but it sounds like you want to save money. There are better places to save money than on your winch system.

What fairlead is recommended for synthetic rope? ...I don't want to be cut in two if the line snaps, so no wire cable for me... Thanks.

What fairlead is recommended for synthetic rope? ...I don't want to be cut in two if the line snaps, so no wire cable for me... Thanks.
An aluminum hawse fairleads.