If you're doing a scale model, I presume you will be using the same propeller and rudder layout as on the original. There are several good mail order model parts companies selling these things - do your measurements to decide the sizes you will need. You will be looking to buy:
If you go to a decent library, you will probably find several books on making model boats.
Before you buy any items, at least do a rough sketch of your boat, so that you can see what the dimensions and space available is going to be. Pay attention to how you are going to open up the boat to get at the insides - you will need to plan some sealed hatches or removable roofs. Then you will need to buy:
Power train
1 Electric motor - probably a 700 or 800 size. Get a Brushed one, not a Brushless.
2 Prop tube and shaft - length depends on your plan
3 Connector between motor and shaft
4 Motor mount (though you may make this yourself)
5 Propeller size depends on your motor and your plan - check for compatibility with the shop)
6 Battery (probably Sealed Lead Acid - SLA)
7 Charger for battery.
Rudder
You might want to buy a commercial rudder assembly - see this example page -
http://www.cornwallmodelboats.co.uk/acatalog/graupner_rudders.html - or make your own.
Radio
You should pick a 2.4Ghz set - that is going to be the cheapest and easiest to use. Here are two write-ups for some common ones used on Mayhem:
http://www.modelboatmayhem.co.uk/forum/index.php?topic=27616.0http://www.modelboatmayhem.co.uk/forum/index.php?topic=25779.0What that will give you is a Transmitter (Tx) and Receiver (Rx). Together these are often called a 'combo'. The Tx usually has sticks which you move, and when you do, the Rx puts out a signal on a set of pins built into it. Some Txs have a wheel. For 2.4Ghz you need to buy the Tx and Rx as a pair, and they will be specified as N-function, where N is usually between 2 and 6. This means that, for a typical 4 function set, you can do 4 things on your boat. Motor speed is one, rudder is another. You may want to switch lights as a third, or operate a boom crane? Because aircraft need 4 basic control functions (rudder, elevator, aileron, motor) a lot of radios with sticks are 4-function - there are a lot of radios designed for cars which are 2-function. So long as you stick with 2.4Ghz sets you can use any of these - don't buy a 35Mhz set which is for aircraft only.
Your receiver will just put a signal out on its pins. To make that signal do anything, you need to connect an actuator to the pins. When you just want a movement, the actuator is called a 'servo' - these are quite cheap - under £10. If you want to control a motor, you need an Electronic Speed Controller (ESC). These may cost £20 or £30 - and you need to get the right one for your motor. In particular, you need a Brushed ESC for a Brushed motor. Again, a shop or this forum will advise.
With a Tx/Rx combo, one servo and an ESC, you will have the minimum you need to operate a model boat.