How to prepare to a big trip in terms of Visas

Congratulations, your travel world will open up considerably after you receive Australian citizenship.

The following Wikipedia page has a map and a lot of good information: Visa requirements for Australian citizens. Your world will look something like this:

The countries in green you can enter without a visa (note that for the US, you will need an ESTA which is US$14 and is not technically a visa (it is permission to board a plane to the US). For most of the green countries, you walk up to the border control, present your Australian passport, the border guard will ask how long you plan to stay in the country and perhaps what you will do there, and they will (hopefully) let you in. Sometimes you need additional documentation like accommodation details.

For travel to Russia or other countries (for example Cuba or Mongolia) where you can enter more easily with a Russian passport, see I have two passports/nationalities. How do I use them when I travel?.

Most countries have a service for citizens which will provide basic travel-related information for all other countries in the world. For Australia that is Smartraveller, a service of the Department of Foreign Affairs and Trade.

On this site you can enter the name of a country and receive information relevant to Australian citizens, such as:

• Visa requirements and where to apply
• Crime and terrorism information
• In-country travel information (e.g. driving, rail or air travel)
• Legal and health information
• Embassy and consulate contact information

You can look up any country on this site to find out quickly this basic information about the country, written expressly for Australian citizens.

First stop is USA - and I believe there is a Visa Waiver Program, that allows me to enter freely (to a certain exempt). I will need to check on their website prior if everything is good with my passport - and proceed. Then in the airport I will need to get a stamp, right?

While this is the truth it is unfortunately not the whole truth. It is true that you probably do not need a Visa (unless you have some history that makes you ineligible for the Visa waiver program or are traveling by private aircraft), but to travel to the US on a commercial air or sea carries you do need an advance authorization known as an ESTA which the US government insists is not a Visa. This is applied for on-line.

Under the visa-waiver program you are limited to 90 days per visit, there is no formal limit on the frequency of visits or their cumulative length, but nevertheless you risk entry denials if you try to spend too much time in the US. Exactly what "too much" means is down to the discretion of the border guards. There are also some special rules designed to prevent people doing "visa runs" to nearby countries.

Canada has a similar system which it calls an ETA.

Next stop is Iceland. I am not sure about it... Any hints?

Iceland is part of the Schengen area, currently you don't need any advance authorization to visit. The Schengen area has plans for an ESTA-like system called etias but hasn't actually introduced it yet.

The Schengen area normally (there are a few exceptions but I haven't looked up if there are any that apply to Australians) limits visitors to 90 days in any 180 day period. Note that this limit applies to the total time spent in all Schengen countries and the days on which you arrive and depart both count.

Finally, Europe - starting with Scotland (UK),

The UK allows you visits of up to 6 months (3 months if you enter through the republic of Ireland) without a Visa or other advance authorization. Similar to the US there is no explicit legal limit on the number of visits or their cumulative length, but spending too much time in the UK can cause you problems with the border guards.

then France, and finishing up in the Czech Republic.

These are both in the Schengen area, so see what I wrote above in the Iceland section.