I have used a strap and a chain both on various types of post with good results. The selection process of strap vs chain is typically based on the type of post/lack of damage wanting to do to the post.
Several factors to consider:
1) rear ballast is extremely important as the resistance of the post will want to pull the rear tires off the ground. Also if pulling from a corner of the loader is the tipping factor!
2) while T-post are fairly easy to straighten, it is relatively easy to break round, square, and wood post. The simple fact of raising the loaded changes angles and the pressure of the post creating bend on metal post and breaking on wood post. This is often at ground level, but can result in pieces above ground level which is likely to be unacceptable and create additional work.
3) concrete set post make all of the above more likely to occur.
On chain or strap wrap your post/chain in a manner that you pull from the bottom of the wraps and as pulled it tightens on the post. Wrap several times and low enough that the length of strap or chain allows the bucket/forks/whatever to begin the lift just above the top of the post. The bucket against the post increase the risk of bending/breaking.