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

I've looked at the Diana 56 and to be honest, I can't get over the plastic front sight. It may be a great gun but I can't get over the plastic sight. It just looks so out of place on a $700 gun. Even if it was the greatest gun in the world I know it will bother me, I'm just anal that way. Thanks for the imput though. Have a great evening. Kevin
 
Don't forget the Fwb 124. New ones are a bit more expensive now but it's a light, easy to cock, easy to shoot, accurate rifle. Can't even estimate how many tins of pellets have been through mine. It might not be best for certain competitions but it's plenty capable. Would be a lot better choice for boys than the heavy beasts you listed and very little, if at all, less accurate.

Another rifle that's similar in size and power is th Hw 35. Very nice shooter as well.

Btw, I own the TX 200 Mk 1, LGU, and BSA Superstar. I really like the TX least even though the trigger is best. I prefer the Superstar of the 3 but tend to shoot my 124 much more than any of those 3. I keep a peep sight on the 124 so the balance isn't messed up. 

Bob
 
Another vote for the RWS/Diana 54/56!

BTW the 56 comes without sights not with a plastic sight. The 54 does come with a plastic front sight but it is easily replaced with a muzzle brake or silencer. My favorite thing about the side lever platforms is the ability to have a bipod on a springer. The fact that the sled makes them impervious to hold sensitivity is a wonderful bonus. This is the reason FWB 300s are still popular 30 years on...




 
I would personally take a hard look at the HW98. It's a breakbarrel platform - it's an HW95 action with an upgraded stock and barrel sleeve making it a bit more docile.

I liked that rifle more than the TX200, HW97 or any other heirloom springer.

I have an RWS 48 in .177 and it personally shoots a little hot for my tastes. It's about 18 ftlbs. It takes more effort to shoot accurately than my Beeman R10, HW97, or RWS 34.

That being said, you really can't go wrong with any of the choices listed above. They're all fantastic and much of it comes down to personal preference.
 
My vote would be AA TX 200 MK I I I standard length or HC. I've owned 3 and they are amazing guns to shoot. Allow alittle in your budget for a tune after you've shot the gun for a month or 2. These guns @ 12 ftlbs. are just a pleasure to shoot. A little on the heavy side maybe for your kids to shoot....don't know if you mentioned their ages. Easy to work on also. The Pro Sport is basically a nicer (notice I didn't say better) TX.....and alittle harder to cock. Hw 97 is probably just as good as the AA and if you want to take it out and knock it around the synthetic stock would probably be a great choice. But for a gun you want to keep and pass down to the kids someday....either AA in walnut....heirloom. IMHO of course. 
 
The Air Arms TX200 MkIII is a beautiful “bit-of-kit” as the British would say. The wood stock and the bluing are exquisite and the trigger is second-to-none. Unlike less expensive air rifles that I’ve owned, the TX200 performs consistently well and is therefore very predictable. I know exactly what to expect at different ranges and in very diverse conditions. It’s a pleasure knowing that if I do my part, the TX200 will reward me with exceptional accuracy. The TX200 is a heavy air rifle as both the underlever cocking mechanism and the barrel shroud are made of steel. Including the Hawke scope, my TX200 weighs-in at just over 11 pounds, this makes off hand shooting and trudging through the woods more difficult. Living in the US has provided me with the opportunity to hunt and take Armadillo, Chipmunk, Grey Fox, Possum, Porcupine, Prairie Dog, Raccoon, Rabbit, Rat, Skunk, Squirrel, Turkey and a Plethora of other birds. All this was done with head shots using my TX200 and the twenty-two caliber H&N Baracuda Green pellets. I’ve developed reasonable expectations and a good understanding of the limitations of a spring powered air gun. I’ve done my part to attain exceptional accuracy and then maintain that accuracy through proper care of my TX200. Would I recommend the TX200 MkIII; absolutely, she’s a “beautiful bit-of-kit”.
 
If your thinking underlever then you may want to stay away from AA and Walther as their loading ports are really geared for a right handed shooter as they don't seem to think left handed shooters exist. The hw97 port is more open on the left side making it easier for a left hander to load the pellet into the breach.

I just picked up a hw98. Nice gun, heavy but I did notice its tends to make my off hand shooting more steady.
 
Beauty is in the eye of the beholder, but I prefer the AA TX200 over other springers. It’s not only looks, but they shoot so darn smooth and accurate. Everything just oozes quality! Honestly, I’ve owned many (somewhere around 50+ or so in the past decades) air rifles (including the HW 97 and 77), and they have all left my collection at some point, while the TX200 (.22 cal) is still in my possession. I’m even thinking about selling my last PCP to get a Pro Sport in .177. Shooting springers is way more fun than PCP’s, but that's personal also.

The Air Arms rifles are the best IMHO, and there's nothing that can top them. 
 
Just got an HW97 with the synthetic pistol grip stock from Krale. It's at 20 fpe only. Want to use it for WFTF so ordered a Vmach 12fpe tuning kit as well. Delivered to calif in 4 days. Set me back $540. Currently disassembing it for the tune. Heavy but well made. It's my first german springer

You might be thinking 20 joule or 14.7 fpe.