Help with board choice

I want to be able run 4 solenoids, like this only with 4:

It looks like with something like the motorbee I would not need to use the breadboard? I need to keep costs low so I'm fine using the breadboard if need be.
So what's a good inexpensive bet for me?
Thanx in advance

Any Arduino will work so I'd use the UNO or Leonardo. Unless your solenoid coils work on 5V and 30 mA or less you will need a transistor to drive the coil.

You don't need a breadboard but it would be easier to design your transistor circuits on one. Without the breadboard you'd have to solder the circuits together and that makes them much harder to change if you get it wrong the first time.

Thank you.
I need a solenoid with strong push force, I'm looking at one like this:
http://www.amazon.com/Amico-Stroke-16000GF-Solenoid-Electromagnet/dp/B0094GB4MO/ref=sr_1_14?ie=UTF8&qid=1355449894&sr=8-14&keywords=solenoid+push+gf

it's 48V 5.05A, what kind of transistor will I need?

For that voltage and current you will probably want a MOSFET for a driver. Look for a Through-hole, Logic Level Gate, N-Channel MOSFET that can handle 48V (or higher) and 5.05A (or higher).

The lowest cost ones available immediately from DigiKey are:
Fairchild Semiconductor FQU13N10LTU $0.71
Vishay Siliconix IRLZ14PBF $0.91
International Rectifier IRLU120NPBF $1.05

You'll also need a 48V 20.2A (or higher) power supply.

Thank you John for helping educate me. I ordered an UNO R3.
So if I went with a lower volt/amp solenoid then I'd just get a transistor rated for that I suppose. I'm thinking now a 12 or 24v, with power provided by an AC wall transformer.

For my parts list, in this tutorial he also uses a diode and a resistor, I'll need those as well?

When you turn off a solenoid the magnetic field collapses and generates a reverse current spike. The dode protects the switching transistor from the spike. You will need one per solenoid.

The resistor protects the Arduino pin from the transistor drawing too much current. You will need one per transistor.