Welcome to GTA Cruizer,,, nice to have you with us.....
With 450 to spend you have quite a few options when it comes to quality hunting air rifles,,,,
With regard to the 3 specific rifles that you mentioned.......
I own a .22 cal GAMO 1250 (older version of the Hunter Extreme - same power level) and it is one heck of a hunting rifle. It's a powerhouse for sure and mine is deadly accurate. It is a large, heavy rifle though, especially after you top it with a suitable variable power scope to take advantage of it's power and range. I personally wouldn't advise getting the rifle in .177 caliber, the .22 is a much better caliber to take advantage of the power the rifle has. Others may disagree with me regarding the .177 in this rifle but I just feel the .22 is a better choice. You could use the heavier .177 pellets but I'd still go with .22 If you do get a Hunter Extreme do yourself a favor and order one of Bobs (charliedatunas) GRT III triggers,,,, it's a drop in replacement and it will transform the rifle for you instantly, making it much easier to direct all that power accurately.
I recently bought a .20 cal RWS 48 and I can't say enough about the rifle. While the rifle is indeed a bit heavy I find it to be an extremely comfortable gun to shoulder and shoot, I like it's shorter length, and the power and accuracy of the rifle are outstanding,,,, as is the trigger. It is a superb small game hunting rifle without a doubt. I recently installed a sling on mine to help with the weight issue and it's worked out great.
The RWS 54 is also a superb small game rifle. I don't own one but I've shot one many times and they are sweet indeed. As you know they have all the benefits that the 48's have except they have the added benefit of hardly any recoil. The 54, as you know, is a side cocker and something to keep in mind is that a break barrel is much quicker to reload while hunting if you need that "second shot". I can reload my 48 quite quickly but it did take me a bit of practice.
I feel the quality of the RWS rifles is superior to the GAMO rifles and for that reason if I was limiting myself to the two brands I would probably go with an RWS. The RWS triggers are far superior to the stock GAMO triggers as well and we all know how important a good trigger is.
Like I said, with 450 to spend you have a variety of options,,, makes, models, etc.
I'm sure some of the other members will chime in and give you their take on things. After you get some feedback on your question take some time, cruise the internet air gun dealers and look around at your options. I'm sure you'll find the right gun for you.
Again,, nice to have you with us here at GTA, it's a great forum, you'll like it here

Jeff