If you have the stock Motorcraft 2150 2v carb I would keep it and rebuild it. It's a good carb more than adequate for feeding the 360 and easy to rebuild and easy to tune. Also more off camber friendly off road than any 4v carb. You'll need a good carb rebuild kit. Instructions come with the kit. Insure it comes with a new power valve and if not buy the needed pv. Buy a real carb cleaning set up. You want the gallon can of Gunk or Berrymans with the soak basket in the can. It's reusable. Once disassembled soak the carb thoroughly then flush with lots of fresh water, blow out all the passages with compressed air. Dry thoroughly, reassemble, tune. Don't bother with just spray can carb cleaner, it doesn't soak anything off.
None of this hard or techy Just work slow, pay attention to detail and "cleanliness counts".
DO NOT waste your money on an auto parts store rebuilt in Mexico carb. Expensive and generally Junk. Now a days prolly near $300. Odds are <50:50 you'll get a good one.
Even Napa gets about 1/3 to 1/2 of their rebuilt carbs returned.
The Weber 32/36 is a fine carb swap for a 258 I6 but very expensive and you'll need the adapter and cable linkage. I wouldn't risk the $$$ on a 360. I also wouldn't recommend a 4v swap. Unless you go all out $$$ with the correct intake manifold, exh and cam not really much HP/performance again over the 2v MC 2150 and more grief to tune. For an all around use good running 360 stick with rebuilding the 2150. If you're just not into doing the rebuild yourself have a local shop do it "in house". Prolly still cost you a couple hundred bucks but it's still better than a auto parts store Mexican rebuilt.