Two words you need to know: 
 Sensitivity and Selectivity. 
 After that, the rest are just options.  

That's sort of a bold statement but basically it's true. I'll make the assumption that the scanner covers the frequencies you want to listen to.   If you can't hear the train that's a half mile away because the sensitivity of your radio is so poor, then a fast scan rate won't make rail fanning with a scanner much fun.  Likewise, if you can hear pretty good but you also hear everything else between DC and daylight interfering with what you want to hear, then a "Priority channel" is sort of useless also.  Let me see if I can explain some of this in some simple terms.

Before jumping into the fire let me offer this disclaimer.  "Your mileage may vary."  The manufactures make measurements in laboratory settings under ideal conditions.  If you've ever used one of the FRS radios you know they are advertised as "2 mile" radios but you'll never get that much range unless you are talking hilltop to hilltop.

SENSITIVITY refers to how sensitive the radio (scanner) is to radio signals.  It's a measurement of how much signal coming into the radio is required to give you, the user, an audio signal that you can hear and understand with a minimum of noise.

What are the standards used to compare the sensitivity of radios?  Generally the manufacturers will specify how much of a signal is required to give a specified noise characteristic at the output.  The first part of the measurement is simple.   The levels are measured in microvolts (1 millionth of a volt) or fractions of a microvolt.  When looking at the specifications of a scanner, you'll probably see the number are different for different bands of frequencies.  Scanners are optimized for the most common frequencies used by users (police, fire, rail, etc...) and suffer slightly on the not so popular services (data transmissions, river traffic, military aircraft, etc...)  For rail fans, you should be looking for a scanner that has a sensitivity between 0.1uV and 0.3uV sensitivity on a band that includes 161Mhz.  The smaller the number, the better.  I have an old scanner with a sensitivity of 1.0 microvolt (uV) at 161MHz.  I have another radios with sensitivity of 0.1uV.  The one with the 0.1Uv sensitivity is far superior.  

The second part of the specification can get a bit confusing.  The technical details can get rather lengthy but I'll try to hit on them and then give you the practical aspects.  Some manufactures use SINAD in the benchmark and others use S/N ratio, or even (S+N)/N. Comparing these is sort of like comparing apples, oranges, and pears.   SINAD is SIgnal + Noise And Distortion.  S/N is a ratio of how strong the audio signal is compared to the noise.  (S+N)/N is similar, just specifying the that the output signal measure with the signal and noise and then compare that with the noise only reading.  If you want to know the nitty-gritty about these just do a search on the internet and you'll find enough stuff to keep you confused for awhile.  When comparing radios, one might specify SINAD 12dB at of 0.2uV while another might show 0.2uV for 20dB S/N.

What's it all mean to a rail fan?  It's really pretty simple.  Look for the lowest level of signal (remember, 0.1uV is better than 0.15 or 0.2uV) and forget whether it's SINAD  or S/N.  My ears don't measure SINAD and I doubt if yours do.  SINAD and S/N are just different ways to measure how much noise in in the output of the receiver when there is a specified amount of unmodulated signal at the input.  In the real world, two radios with 0.2uV sensitivity, one measured with a 12 dB SINAD standard and the other with the 20dB S/N standard, both will probably sound about the same to the user.  In the real world you're going to have ambient noises that are not measured in the lab.  The sound of the air conditioner or road noise in your car, the wind blowing, industrial noises, cars going by, or who know, even a train.  

Another important contributor to the "Sensitivity package" is a good antenna system.  If your antenna system only produces 10% of the signal that a good antenna would, your system is going to suffer.  

One thing I have notice on some "NASCAR" or "Race" scanners is that they don't show a sensitivity specification.  RadioShack has a document on their web page that talks about the advantages of NASCAR type scanners and one of the so called advantages is that they use a very short antenna.  One of the advantages is that the short antenna doesn't poke you in the ribs.  The other advantage is that it reduces the sensitivity of the scanner so that you are not as likely to receive interference from outside of the race area. After all, everything you want to hear at a race is within about 1 mile and is line of sight.   Personally, I would be reluctant to purchase a radio that does not have an advertised sensitivity, especially if the documents that come with it say that it has been desensed on purpose.  On the other side of the coin, I suspect that if you put a decent antenna on any of the NASCAR or race scanners, they probably will perform OK.

The table below is a work in progress and may become out of date rather quickly.  I've tried to include some of the more popular or common scanners and receivers on the market.  Many of the models listed cover additional frequencies but I have limited this data only to those frequencies commonly used by rail fans.  The list is in no way complete and I can not assure that all of the data is correct.  Street prices are those I found when I entered the data on a particular radio.  You can probably find a better price if you search enough.