Welcome Mr. Peach
Wonderful little car you have and you'll be glad you bought into the Honda family.
My opinion may differ from others but I'll lend it to you anyway.

Put simply, if you're on a low dispensable income I would suggest holding off on modifying the Breeze and save for something newer and all round a better package.

If you've simply fallen in love with the EG shape and can't see yourself in another car, start saving your dollars. Honda's can be some of the most expensive cars to modify in Australia simply due to the low supply of quality parts.

The run down on engine transplants into your Breeze is pretty straight forward to me.
1. Your car is not running EFI(Electronic Fuel Injection) and therefore you can't just drop an EFI engine in and drive away. You'll need an EFI fuel tank and fuel lines to name a few of the parts.
2. You can't just grab the engine and plug her into you standard wiring. You will probably need a matching ECU(Engine Control Unit) and the wiring to go with it.
3. The Breeze is great for sleeper status. Leave the stickers on, a stock looking exhaust, keep it quiet and chuck in a B18C or B16A engine(along with the needed brake/suspension upgrades) and watch other drivers jaw drop as they just got beaten by something resembling their hairdressers car or grandma's shopping trolley.
4. Being on your green P plates in Victoria knocks the idea of an engine transplant straight out of the picture, unless you enjoy running the risk of being caught. Other people have done it, I personally wouldn't. It really depends how lucky you feel and how well you think your local cops will know a Honda engine bay.
5. Don't forget insurance, if you haven't got it then get it. If you're only on third party then you are allowed more freedom than a full comprehensive policy but it pays to enquire about what you would be covered for, before modifying your car.
6. With the added power of a new engine you definitely need to at least swap out those rear drum brakes for some in the disc variety.

The price of an engine varies from seller to seller and always reflects the history, quality and parts included. Look around on these forums and don't be afraid to check out forums from the USA(they've done almost everything possible with the EG Civic). There is a wealth of knowledge all over the net about Honda engine swaps. There's even a book published about them, spending 50 bucks on that book could save you a lot of time and hassles.

To conclude, many of the answers you seek are on this forum. The search feature isn't the best system but give it a good work out and you'll be well on your way to beginning your knowledge of Civic EG Engine swaps.