Can someone explain chain ring/ compact cranks...

I'll take a shot...

Your terminology is slightly off, you are talking chain ring (gears near the cranks/pedals) and cogs (small gears on the back wheel...  the group of which is known as the cassette, I think).  I call the parts of the front that aren't the chain rings the crank and the arms going to the pedals the crank arms...  ( I may be slightly wrong, someone will correct me though)

What you are choosing between is your gear ratios, big number up front and small number in the back mean tall gearing (aka high gear, aka slow pedal fast speed, aka 5th gear in your car) Smaller up front bigger in the back mean short gearing(aka low gear, aka fast pedal slow speed, aka first gear in your car)

So since you are a near hills and a sounds like close to a biking noob, you may want the lower gearing that the triple allows (the 30 front - 26 rear granny gear vs 39 front - 25 rear)... 

From what I understand a "compact crank" allows the use of smaller front chain rings, is probably lighter...  Not sure though...

You also want to check what model of components you are getting on each bike, other people know more about this then I do, but it may be worth getting the double even if the gearing is a little harder for you until you get some miles...

  -Andy

Gears are all about being able to maintain a comfortable pedalling cadence no matter how fast your bike is moving.  When it is moving fast (e.g., downhill), you want more teeth up front on the chainring and fewer on the cogs in the back.  Otherwise you will have to pedal very fast in order to move the bike any faster than gravity would do on its own.  Conversely, on a long steep climb you want fewer teeth up front and more in the back so that you can keep up a reasonable cadence without having to come up with a lot more power.  You can check out a calculator here that you can play with to see how the different combos overlap or change things.

From what little you have posted, I'm not sure there is a convincing reason for you NOT to get the triple.  Another option is to get a "compact" crank which allows smaller chainrings up front (e.g., 34/50)--giving up some "top end" for more "climbing" gears.  The reasons that might be attractive over the triple is lower weight (probably not a big deal for you) and generally less "fussy" maintainance (triples tend to require more 'tweaking' to keep them shifting to all the rings well).

A compact drivetrain comes with a smaller bolt circle diameter on the cranks (the bolts that hold the chainrings on the crank.)  This allows the use of smaller chainrings than a standard double.  The 39/53 is a standard double.  A 34/50 would be more common on a compact drivetrain.  

Take the number of teeth in the front and divide by the number of teeth in the back.  Assuming both bikes have the same size wheel and the same length crank arm, this number will let you compare how easy it will be to climb a hill in that combination.  Lower numbers are easier.  The double has a low gear ratio of 1.56 while the triple has a low gear ratio of 1.15.  Much, much easier to get up long steep hills on the triple.

A double with a compact drivetrain is equivalent to a triple but without all the extra weight and complexity that comes with that middle chainring.

To determine how fast you can go in a gear you need to calculate gear inches.  This is the number of inches the bike will move per revolution of the cranks in that gear.  It is the number of teeth in the front multiplied by the diameter of the rear wheel divided by the number of teeth in the back.  For example a 53-11 on a 700x23 tire will get you 53x26.3"/11 = 126.7" per rotation of the cranks.  Using the 39-25 on the same bike you get 39x26.3"/25 = 41" per revolution of the cranks.  Multiply by the rpm you pedal at to get inches per minute.  Beyond this you have to convince Obama to go metric because my head hurts trying to convert inches per minute to miles per hour at 8am.  

Don't discount yourself for being a girl, there are some girls around here that can make many of the guys look slow.  If it's hilly and you don't have a lot of experience cycling, use the triple.  

Gear inches is a system that assigns numerical measurements to bicycle gear ratios, to indicate how low or high a gear is.  Gear inches has no current physical significance; it corresponds to the diameter in inches of the main wheel.

To get your speed you need to consider the circumference of the wheel.  In your case just multiply the result by Π (pi ~ 3.14).

20.24 x 3.14 = 63.55 km/hr or ~39.49 mph.

20.24 x 3.14 = 63.55 km/hr or ~39.49 mph.

I'm sorry but this answer is incorrect.  Generally your mixing up power and force.  For a given bike/rider/position you need exactly the same amount of power to go a given speed whether your cank arms are 150mm or  180mm.  What canges is the amount of instantanious force you need to apply to the pedal to achieve that power.  Essentially to achieve a given power at a given gear ratio with a longer crank arm you will be applying a lesser force over a longer pedal circumference.

I've got to go with Kathy on this one. My triple is finicky and has never really worked right. Glad yours works, but for others they are definitely finicky.