Hi, getting a full suspension mountain bike isn’t a question as simple as which one is the best.
First, let me start by saying that you might want to up your budget. Almost all full suspension bikes of any real quality will cost you at least 1000 dollars. Also, when you are looking for a full suspension bike, you should go for the used market. PinkBike and Craigslist are two solid options when searching for a used full suspension. You can often score bikes that would normally cost thousands of dollars for less than half their original price if you are patient and do your research. When looking for value, the used market has some very solid options. Just be warned as there are plenty of scams out there that will sell you a bike that seems good at first but has a lot of issues.
Second, when searching for a full suspension you need to know your style of riding. Do you want to ride smooth trails with lots of climbing? Do you want to tackle nasty double black diamonds and sketchy features? Are you looking to hit big jumps and drops? There are many different types of full suspension mountain bikes. Cross country, trail, enduro, downhill, and free ride are the main types. Each different bike is styled towards a different type of riding. Cross country or XC bikes are great for long, hard climbs with flow and smooth decents but lack the suspension to get down gnarly tech or large obstacles. These bikes often have 80-120 millimeters of suspension travel. Trail bikes are best suited for the average mountain biker looking for a bike that can climb well and decend well. These bikes range from 130-150 millimeters of travel. Enduro bikes are for the rider who wants to hit nasty tech and big jumps. People who own enduro bikes typically are more skilled riders who like to take to the air and ride sketchy features. These range from 160-180 millimeters of travel. Finally downhill bikes. These are NOT meant for climbing. Only use this if you are at a downhill park with a ski lift. They are meant to handle almost anything as long as it’s downhill. These have 180-200 millimeters of travel. In order to find out which bike is best for you, I highly suggest going to your local bike shop. They can help you find the perfect bike best suited to your style of riding. People at bike shops love and know everything there is to know about bikes.
Finally, I do have a few recommendations for you to look into. Trek’s fuel EX lineup has done great trail bikes that come in every size you can imagine. This line of bikes has options from 1800 dollars to 8000+ dollars. Specialized’s StumpJumper lineup also has lots of good trail bikes at various prices. My real recommendation though is that you should talk to the folks at your local bike shop. They can help you find the bike that’s perfect just for you. Also, back pain doesn’t necessarily mean you need more travel. It might mean your current bike is the wrong size or your posture on the bike could be causing it. Good luck on your search!