You do realize it is a kit without a battery included? The battery is the most expensive part of the kit, a good LiFePo battery can easily run $300+, take a look here: http://www.pingbattery.com/servlet/StoreFront
Some say these are good, so say they are not, but they have mostly positive review's for the price. So count as a bare minimum for the kit + battery to spend around $600. That is for you requirements, that is a kit that will take you up to about 25-27 mph on flat ground with no headwind. If you want more speed, prices go up, you namely need a controller capable of higher voltage, a better motor also capable of going higher in voltage an power and speed, in that case you're looking at a minimum $1000 for good quality parts, easily more.

Talking about distance, I can cover on my own power around 5 miles in 20 minutes, so with a good setup you should be able to cut that at in half to about 10 min. In any case, if you wish to do it right, what you absolutely should use for good performance is a LiFePo battery, as ordinary lead acid batteries have a lot of problems in practice. The most notable are weight, they are tremendously heavy, and poor performance cycle. An 10 Ah LiFePo battery will be about 10 lbs, while the equivalent lead acid will weigh between 50 and 60 lbs, while having much worse performance. With batteries, discharge current is important, and lead acid cannot take high currents (high speed riding, quick takeoffs, sustained hills) for very long before it kills them. If you ride lead acid battery on a regular basis at high load (and with high speed and some hills you would definitively do that), you will kill that battery in as few as 150 to 200 charges. It's performance will degrade fast, and at about halfway point of 100 cycles, you will have maybe around 70% of starting capacity, that you won't be able to use as voltage drop will be too severe for controller to work properly. In reality, lead acid batteries are a very bad idea for any trips over 5 miles total, and for hills especially as range drops to practically nothing once you drain them hard for a time.

Also, look at rear hub motors as a start, front ones can be a bit finicky to ride, and you must have a proper steel rigid fork upfront, no suspension forks or aluminum or carbon. There are problems with wires continually twisting as you move the steering around, and the length of the wires from controller to motor makes for some additional losses due to higher impedance in longer wires - usually controller is mounted around the seat tube, so power phase wires have to be longer to reach up front.

Controller is used to drive the motor, and to regulate how much current the motor is going to draw from the battery, and to regulate the speed - from standstill, over gradual acceleration, to full power, and everything in between.

I gave you the rough basics here, for much more info and everything you need to know to make the proper decision, take a look here, register and read, you will see there is so much more you need to know before doing your first conversion: http://endless-sphere.com/forums/
That is the most complete forum about e-bike conversions and builds that I am aware of.