What company makes the best air guns?!

With your price range the best you could get is probably a break barrel air rifle just like you mentioned. However I did see a Marauder in .22 cal on the classified section for 350$. The companies you listed such as Gamo are not really the top IN MY OPINION. However many of the companies you listed are a great value for beginners! I suggest you look at
Daystate: http://www.daystate.com/ 
FX Airguns: http://www.fxairguns.com/
Edgun: http://www.edgun.com/
JKHan Jihad: http://jkhanairrifle.com/main/index.php
-If your wanting a new level past Gamo and most of the springers from Crossman, the companies I just mentioned are IN MY OPINION the "higher class/best" airguns. 
Also your overall question is very vague. Many different Airgun companies cater to different people and could be the best in their own niches. Daystate for example offers great walnut rifles with amazing accuracy and could be "the best rifled airgun" while FX airguns and other companies have their bullpups+ rifles. Many of the companies have different power, caliber, shot count, looks, price. and many other attributes that make their own guns "the best." So its best not to say which company makes the best gun but to ask yourself, "Which gun would suit my needs the best!" Again this is just my opinion, everyones will be different. Also, these are just companies that popped up off the top of my head, there are many more that I just can't recall at the moment. Good luck finding/researching the rifle and welcome to the forum!
Michael

For one there is not really a "best company" there could be a best gun for a certain criteria but most guns are designed for different purposes. You don't really want an airgun going over the 950 fps range because in an airgun the pellet will break the sound bearier and then destabilize which is horrible for accuracy so rather than Foot pounds of energy you want to look more for accuracy. And most of the manufacturers that put " this gun can go up to speeds of 1200 fps with PBA pellets" the gun might be capable of doing that most likely not though, and even if it was capable of doing that again that wouldn't be good for accuracy. Also with the PBA pellets they are not good for break barrel rifles because since they are so light it is almost like dry firing the rifle and dry firing a springer is not good. So try to stick with the heaver pellets lower speeds and more accuracy because it doesn't matter if you have a 100 foot pounds if you can't hit your target. I hope this helps you some in making your decision just making sure that you don't make a mistake like a lot of people out there. I've also heard that the Crosman 392 pumper is pretty good although it's loud. And i think Hatsan makes some pretty quality springers.
Leo

Most of the brands you listed are entry level brands. More mass market consumer grade guns carried by big box stores. There is a whole world of high end guns that you probably have never heard of. Hang out here and learn for a while. Ask questions, do lots of research and you will get a new sense of what best might mean to you after you see what's available. Just an example of the range of prices you will encounter. You have already seen the lower end ($100-$300) but high end springers go upwards of $1000. And Precharged Pneumatics(PCP) go upwards of $3,500. (plus support equipment.) Some more.
Welcome to the forum. Lots of help available here.

For just a little more than what you've stated, you could get a BSA GRT Lightning XL SE Air Rifle, which is excellent for the price.

It seems as though you have an interest in springers, which is good. Please, YES do not get caught up in the muzzle velocity craze. 
You want ease of use and quality as prime considerations in your first spring gun. The higher the velocity, the harder effort it is to cock, usually along with having a heavier, longer rifle. 

The intellectually honest would admit the best currently produced models are from Germany. HW, or Weirauch, guns are widely considered top-tier. You will still see certain Beeman R-series guns which are simply HW models re-branded for distribution by Beeman here in the US. All that does is add extra cost to you, for the most part.

Second is going to be a battle between Walther's new entries back into the field within the past few years, along with the time-honored Diana, generally imported as RWS/Diana. With but two pricey gas-spring exceptions out of your range, these three are all providing traditional, coiled-spring guns. 

Of the three, the two I would recommend in your range would be the Diana 34 in whatever guise appeals to you. The ones with the T06 trigger are absolutely sweet shooters. Still have a T06 gun now. Or, saving some money which could go to buying a scope, Walther's Terrus. In all ways an impressive value for the dollar, but a trigger more like a typical centerfire rifle from Ruger, or Mossy, for example. 

I really wish the word about higher quality Airguns would get out more. None of the big stores in my area carry anything above a Benjamin trail. There are so many people that don't know about the better quality guns and think gamo and crosman are just it. 

German of English when you are talking spring or gas pistons.

#1 - Don't fall for all of the marketing hype on the packaging. FPS keeps going up because that's what people new to air guns think they want. Manufactures keep shooting lightweight pellets to boost their products. Not what you want, like has already been said. 

Crosman/Benjamin makes a really sweet little rifle (.177 or .22) called a Discovery. It's an entry level rifle to the precharged pneumatics (PCP). A new one will cost around $220. Buy a used PCP pump and you can shoot Walmart Crosman pellets accurately and powerfully all day long. Mine does. 

Google "air gun" and see some vendors like Pyramyd Air and you will see lots of choices. 

My .177 Hatsan Striker would have nudged the 1000fps as their marketing says and after a 100 or so pellets I have no doubt it would have got there but accuracy was going out the window. I don't mind tinkering so I stripped it down, cut 2 coils off the main spring, replaced the steel tophat with one made from a Delrin type material, give the tube a bit of a polish, re- lubed the spring, re- worked the trigger and it now shoots H & N Barracuda Match ( 10.35grns ) pellets at a consistent 800fps. It is an absolute tack driver out to 25-30 yards if I do my bit. This rifle with scope cost less than 300 Aussie dollars, you get what you pay for in this price bracket but they can be made to shoot very well if you want to work on them, as for who makes the best air guns, don't know the answer to that

If I was to do it all over again.
I would jump into a pcp right away.............. I have many under levers and break barrels that I will never use..
because I was trying to get by cheaper.... I got a Discovery .22 and my whole world changed.... 
I now wish I saved a little more and got a rifle that I can shoot.... 

"GLPalinkas"#1 - Don't fall for all of the marketing hype on the packaging. FPS keeps going up because that's what people new to air guns think they want. Manufactures keep shooting lightweight pellets to boost their products. Not what you want, like has already been said. 

Crosman/Benjamin makes a really sweet little rifle (.177 or .22) called a Discovery. It's an entry level rifle to the precharged pneumatics (PCP). A new one will cost around $220. Buy a used PCP pump and you can shoot Walmart Crosman pellets accurately and powerfully all day long. Mine does. 

Google "air gun" and see some vendors like Pyramyd Air and you will see lots of choices. 
=====================================================

THIS is your best advice, I believe. Best way to learn. Then a year or two from now can make a change... if you decide to change (or more likely, "add"), you will be far more informed. Discovery was made to hand pump... low pressure, very easy to pump the Discovery. Accurate, reliable, easy to shoot.

Click to expand...

PCP is different than spring, not necessarily better.

PCP requires a source of compressed air, like a handpump or an air tank, both of which cost extra after the gun purchase.
PCP is hardly hold sensitive to the point of being negligible, so it is much easier to shoot accurately than a spring gun.
PCP can be made more quiet than a spring gun at the same power level, because it doesn't have big heavy moving parts.

A gas spring (IGT) is still a spring, I find that there is hardly a benefit to a gas spring compared to a steel coil spring that is worth the extra money for the gas spring.
Gas spring guns can still be harsh and hold sensitive, while a well-made and/or nicely tuned steel spring gun can be smooth and a joy to shoot.
And neither gas nor steel spring guns need a pump or air tank to shoot, as opposed to PCP.
You already know about the pellet speed ideally below 900 fps. Don't fall for the "but more power!" in spring guns when choosing caliber, because more power usually means harsher shot cycle and more hold sensitivity. A .177 pellet to the brain kills a whole lot quicker than a .22 pellet to the jaw.

For all the game that you describe that you want to take, shot placement is absolutely crucial. With a PCP that is easier to achieve, but costs more money. With a spring (any type) gun it will take more practice to be very consistent with your hold (see billydjann's post), but you don't need all the air charging equipment.

Here is a thread you may find useful: http://airgunnation.dev/topic/why-air-rifle-guns-over-fire-arms-guns-what-are-the-advantages-of-air-rifles/

This one too: http://airgunnation.dev/topic/why-airguns/

How is Steyr not in the conversation? I love me some FX, Daystate etc. but if price does not matter they are the Ferrari.

Well @$#% I missed that part. haha Makes a lot more sense. Now I need to make a post about best guns period.