PC's have the advantage that you can get more bang for your buck, but if you're not gaming or engaging in processor-intensive tasks, like video/photo editing, then you probably won't really need it.
The laptop's obvious benefits are portability, taking up far less space, and also consuming a lot less power. For what you need it for you don't need to spend a lot of money on a high-powered one either.
Sounds like a laptop is the way to go for you. I ditched my PC for a laptop years ago and haven't regretted it at all. I'm only just setting up a PC again now, but that's being done on the cheap and for the purpose of photo editing, which my laptop just isn't that great at. Apart from that, the portability and the amount I save on space is just fantastic - not to mention it uses
As for internet, I wouldn't touch anybody other than Telstra for wireless internet. Any other provider is simply too hit-and-miss. If you think of going that route, try to find out which Telco has good 3G coverage in your area. Even then it's still risky, but at least you're not locked into a contract so if you don't like it you can then sell the dongle on Ebay or something.
If you don't use your home phone much then there's no real need to keep it - you may find it's worthwhile to switch to a naked internet plan (however you don't really save money over the homeline basic plan, but you tend to get more bundled data) and lose the phone. Otherwise, many ISP's will allow you to bundle your home phone with them for more download - only catch is that the phone line then costs $29.95 (not sure what you're paying now just for line rental, but the cheapest connection is about $21p/m).
Of course, you then have contracts and connection fees. However, if you only use a few gb per month you may find that wireless is sufficient, and may be a little cheaper for a really light internet user. Any more than a few gb, and I'd go for a wired plan. I can suggest a few website which can help your search if you like - otherwise, you could just arrange to relocate your existing wired connection, for a fee.
If you stick with wired (ADSL or ADSL2+), then you'll want a wireless router for the laptop, but these can be picked up pretty cheap, if you don't already have one.