Well, there are lots of features I look for in a rifle. I haven't found them all in one rifle yet, so the search continues.
Obviously since we are talking about rifles, accuracy is a real big factor. Rifle shooting is all about accuracy. In my opinion, anyone that doesn't place accuracy as the first thing they consider in a rifle is a rifle owner or rifle collector and not a rifle shooter. Accuracy is the do all and end all of rifles. Without accuracy, you have nothing but a big heavy club. Of course the degree of accuracy you require is a matter of personal needs. We all don't need benchrest accuracy, but it would always be a good thing if we could get it. In another thread I mentioned a standard of being able to shoot into a 20" circle at 500 yards to be a bare minimum standard. The reason we own, carry, and use rifles is twofold: power and long range accuracy. The power is a given, the variable is accuracy. All the power in the world is no good if you can't hit anything. If you can't hit the target at 400 yards, you should have just carried a handgun: it is lighter and easier to carry and you won't hit it anyway. Accuracy is everything in a rifle.
I also enjoy self loading rifles. Probably the second thing I consider in a rifle is where the controls are located. I want to be able to obtain a firing grip with my right hand and be able to access all the controls normally accessed with my right hand from that firing grip. The best example of this is on the AR15/M16 family of rifles. I can take a good firing grip on the rifle and operate the selector switch with my right thumb. I can eject a spent magazine with my index finger and of course I can press the trigger all without losing my firing grip on the pistol grip. By the same token I want to be able to run the bolt from the left side of the gun while continuing to maintain my right handed firing grip. Again, the AR15 is a perfect example. If, for example, I were to experience a Type 1 malfunction, I simply reach up with my left hand and run the bolt. The rifle is still pointed at the target and my right hand is ready to fire. If I do a magazine change, I slap the bot release located on the left side of the gun and I am back in business: all the while the right hand never moves and the rifle is pointed at the target. Another rifle that comes close to this ideal is the M14/M1A rifle. All the same applies with one exception: the bolt handle is on the wrong side. An example of a rifle I am currently playing with that shows poor ergonomics is the HK G3/91. I can't manipulate the selector without shifting my grip of my firing hand. The magazine release is way out of reach of my index finger.
Next would be sights. Obviously the sights are a big factor in actually hitting something and IMO, American military rifles have sights that are far superior to any other iron sights (other than high dollar competitive match sights) that I have used. The best are the rear sights on the M1 rifle, the M14 rifle, and the M16A2 rifle. They are a peep sight that has a maximum sight radius and are adjustable for both elevation and windage in 1 MOA incriments.
Then we get into the rifles ability to accept accessories: primarily optics. Optical sights make a huge difference in rapidly aquiring a target, long range marksmanship, and shooting in low light. I own a lot of rifles just for fun, but if it is what I call, a "serious rifle" then it must be able to accept optics easily. The current state of the art in this department is the picatiny rail. Having one is a big plus. Again, the AR15/M16 has one = good. Note that I am not talking about some half baked chinese scope mount. I am talking about a rock solid, practical scope mount that will allow you to explore the limits of the rifles accuracy and one that does not interfere in any way with the operation of the rifle. The ability to remove or install a variety of optics at will is a definite plus: this requires a rail.
In a self loading rifle, magazine capacity is an issue, but this was figured out correctly long ago. The .30 rifles are most practical with a 20 round magazine and the 5.56 class of cartridges can accept a 30 round magazine. This provides the best overall performance without the magazine being too long or too heavy. More is good, only up to a point. I want the rifle to accept a magazine that holds the practical limit: no more and no less. I also should mention that a on a semi-auto rifle a detachable magazine is better. I own three M1 rifles and really enjoy shooting them. However, I am not about to tell you that the 8 round en-bloc clip isn't a serious draw back. It is immediately obvious.
One of the last considerations for me is the cartridge the rifle is chambered for. For hunting a .308 or .30-06 will handle any hunting I am ever going to do. I am not into the latest and greatest. For SHTF, personal defense, plinking, formal target shooting etc. the American riflles whether they be .308, .30-06, or 5.56 all work great. The above factors are more important to me than the cartridge. The cost of ammunition doesn't enter into my thoughts at all. You might have gotten the impression that I like accuracy. When I am shooting rifles I am seriously trying to hit something. Spray and pray don't enter into my shooting very often. As a result, I don't go through a huge amont of ammo in a shooting session. Basically, for any rifle I am interested in owning: I can afford all the ammo I am going to want to shoot out of it. My eyes and my concentration won't hold out long enough for me to go through a whole lot of ammo while still seriously concentrating on marksmanship.
Reliability: obvious the rifle needs to be reliable. However, I think the internet commandos get carried away with this subject. My rifles don't have to withstand a 500,000 round torture test for me to consider them reliable. I am far more interested in realistic reliablity. Can the rifle fire 500 rounds in a day's shooting and not malfunction ? That is good enough for me. I also realize that with enough dirt, with a total lack of maintainence, with improper lubrication etc, any rifle will fail to function: so again, I don't look for the worst possible case senario and base my decisions on that. I am more interested in being practical: if I provide reasonable care to my rifle, will it function reliably ? I have never owned a rifle that wouldn't, so again, the points above are more important to me than whether or not the rifle can fall into a vat of glue and fire the next day: especially if it means that I have to sacrifice accuracy, or ergonomics to get it.
Bolt actions rifles follow the same pattern: accuracy first and foremost. If the rifle isn't accurate, then all the other neat features or history in the world don't interest me. Then ease of operation (ergonomics) but here I seriously consider how the rifle is loaded. With C&R rifles, this usually means how well do stripper clips work in the rifle. Not surprising is the fact that the best made C&R rifles work the best: the Sweedes, the Americans and the K31s load like a dream from strippers. On the other hand the Russian stuff is hard to find good stripper clips tha work smoothly and quickly. With a hunting bolt gun, all the ones I own load the same way: one cartridge at a time, through the top. Which I don't consider to be good, but there arn't a whole lot of choices out there. I do own two .223 bolt action rifles that have a detachable magazine: a Tikka and a Reminton 788: this is good IMO.
Oh, and last but not least: my rifles much be able to accept and use a shooting sling. Not a carry strap or an old belt, but a shooting sling like a US 1917 sling.
Looks mean very little to me: if the rifle performs, it looks good in my eyes. If the most beautiful rifle in the world dosn't perfrom, you can have it.
