Man, you're giving me flashbacks.

My method for removal was to cut them off about 2' from the ground, then use a BAH to loosen them up a bit, then use a floor jack and chains as some have mentioned to pull them up. Of course that only worked for about 2/3 of them. For the rest I ended up having to rent a jackhammer from Home Depot to break up the concrete poured around the posts along with a pick and shovel to dig down until I got far enough to remove them. In my case, I was adamant that I wasn't just going to cut them off flush with the ground and call it good enough.

But it looks like you have a bit of a wall there that you probably don't want to destroy, and from the sounds of it, there's good advice to simply reuse the posts for your wood fence. That's exactly how the fence was in my yard; I only removed it because I wanted to open up more area. But the metal posts were extremely solid, and it doesn't look bad at all as a finished product.