FAT.I think you'll want a t-post at every panel join on the straight runs, and maybe every other one around the ends. Used ones go for about $2 around here on Craiglist or at auction.
A friend here has an arena very much like the one you describe, all made of 12' panels. He's used it for over 15 years for roping and sorting.
Thanks for the suggestions. Forgot to mention I DO plan on pounding wood posts for the rounded corners and attaching the panels directly to them. T-posts seem like the most economical and easiest solution to prevent panels from sagging on the sides.