Hi wjm,
I agree with the other guys, SWA is always the cable of choice. You can run cables in a conduit, but is is impossible to guarantee that they are (or will stay) waterproof. A DIYer could terminate SWA but it's important to get it right as the armour acts as an earth, either just to protect the cable or the whole installation (see below).
brezzer is right, you can't run phone wire with electric cable. You can buy external grade phone cable (it's usually grey or black), and you could put this in a conduit, or even clip out down the fence. Only use internal grade (the white stuff) if you can be sure it won't get wet.
The size of the SWA needs to be judged based on what you are putting out there, but also has to take into account the distance (from the supply within the house to the outbuilding, not just the distance between buildings).
I would add a few things, though - I would at least get some advice from a sparky, becuase there are issues with this type of work. The external installation should be protected by a 30mA RCD as well as the appropriate fuse or circuit breaker.
In addition (and please be careful how you read this), it's sometimes the case that you do not use the earth from the house, but instead use a local Earth spike outside the garage, coupled with an RCD inside the garage. If you don't understand what this means, please don't guess! This scenario tends to apply when the outbuilding is more than a few metres from the house, or if your house has what's known as a PME supply (it should say on a yellow label by the meter if you have). It's because the earth connection in your house may be different from the earth you are standing on in your outbuilding (ie there could be a voltage difference, so you could actually get a mild shock by touching an earthed socket). I can explain in more depth if you want.
You could consider a compromise - get a sparky to wire the cable out, install the RCD(s) / Earth rod and put a consumer unit in the garage, then you wire the garage.
If you need more advice on this, please feel free to ask.
Cheers
Paul