5/16" X Grade 70 chain is amply strong for any operational use with a 45-horsepower tractor.
$3.99 per foot at Tractor Supply Company last week. TSC also has Grade 70 chain fittings in 1/4" and 5/16" sizes.
Specialized chain fittings are at Ken's Bolt On Hooks:
Ken's Bolt on Grab Hooks <<Accessories>>
I use and like 5/16" Forest/Logging/Choker hooks.
Usually chain is somewhat cheaper at Rural King.
I suggest one 12' length and one 8' length, with a slip hooks on one end of each chain and a chain grab hook on the other end, so you can infrequently link them together in 20' length.
I too keep a 10' length of 1/4" X Grade 70 chain on the tractor for pulling 1-1/4" saplings out of the ground. On saplings 5/16" chain sometimes slips where 1/4" grabs.
Many use a $20 ammo box bolted to the rear of the tractor to store/transport chains. (Drill a rain weep hole.)