I personally would never use anything less than 3/8" chain, 1/2" if you have it. Ratchet binders are far superior - even with a length of pipe on the handle of a lever-type you can't get a load as tight as you can with a ratchet, and then LOOK OUT when you want to break it loose 'cuz you're going to bust your knuckles or something worse.
I use the 3/8-1/2" binders from TSC - a little pricey but what's your tractor worth to you? Not to mention potential for wrecks/property damage/deaths if highway driving. Yes this is all overkill, but... The alternative is far worse.
I always cross-chain if possible - reduces ability for load to 'walk' sideways. Make sure the bound chain section is as short as possible so things don't 'swing' on an arc. I use the 1/2" chain at the front for a little extra security. Always hook to a non-sprung component, as anything with some suspension give is going to hop and walk after a few miles of bumps. Axles, shackles, large suspension pieces. With a tractor you're okay if you avoid hooking to anything with less than a 3/8" mounting pin (check your draw-bar mount hardware).
Remember cast components are more likely to break before forged ones - your hooks are more likely to break than your chain. Make sure your hooks and pins are sturdy.
I never grease my chain tensioners or chain - just spray them with WD-40 after every use. Keep the tensioners in the bed toolbox, and I keep the chains each individually in a 1-gallon RV antifreeze jug with the hole enlarged to take the bunched chain. Leave the handle tho', makes them easier to lug around and pull from under the back seat. As long as you drive the moisture out (hauling in the rain, logging in the snow) and avoid rust you really shouldn't need grease. I've had some chain 50+ years, including one 4' that i found on the highway, and they're all in good shape. I've found 6', 8' and 10' are most useful.
I avoid ratchet straps, even 3,500-5,000lb'ers for anything bigger than a side-by-side. Almost lost my '64 F-100 using straps. Most frame and body components are like a knife after 100 miles or so of rutching around.
My setup has worked good so far - granted my biggest tractor is only about 8,000lbs with a 6' Howse attached, but I've used the same rig to haul 9,500lbs of reclaimed oak and chestnut barn beams 180+ miles without incident.