What are considered to be the best springers for under $800?

You are overlooking something if the LGU isn't thrown into the mix.

What is there to debate? HW97, TX200 or LGU. You can’t go wrong with any of those. If you have to have someone tell you what to buy then you’re going about it all wrong. 

I found a trade for a Diana 54 Air King. Fast , accurate , and no recoil , which does away with all the artillery hold stuff. You can shoot it off of a Caldwell Tripod at amazing distances in the field , and/or in a hide.

That's a very subjective inquiry as it all depends on an individuals taste. I love my TX200's even being a lefty & as said above, "that annoying comb." 16ftlbs though in .22 so I'd say limited compared to RES/Diana rifles in the 48-56 series, 350, 460, etc and tuned used gun is better than brand new to me. Some will say spring guns are 10M rifles & I personally can't use diopter sights although I prefer micro click even if I scope it. Open is fun & I'm golden to 35 for paper or rabbit. I know all my guns will group incredibly with a scope but open is fun. All of these suggestions are great. Ask yourself how much power you want, weight, sights or scoped. I get every spring gun tuned by John Thomas and I'm always happy with it. I've found high end factory to be a bit disappointing in price to shot cycle without his magic.