Flights to Perth can take upwards of 20 hours from the UK, and include at least one stopover along the way. If you're interested in exploring along the way you could look for deals with overnight stays, which sometimes bring the costs down to boot. Perth is generally the cheapest destination in Australia to get to so it may also be worth thinking about getting yourself some internal flights to see more of the country. There is only one airport in Perth and it serves much of the state of Western Australia.
If you want to travel onwards by public transport you'll need to use the airport shuttle to get from the International Terminal to the Domestic Terminal where the public bus departs for the city. You can also arrange shuttle buses from the airport to the city for any number of people, which is best done in advance if you want the fastest service. Once you land you can get hold of a hire car to get you to your hotel, and if you want the best prices on this then it's also best to book ahead. Taxis are available too but are definitely at the pricier end of the scale.
Perth Airport Home Page
You can travel around the centre of Perth for free on the dedicated CAT buses as well as on the Transperth buses within the designated area, so it's really easy to see more of the central areas. Further afield, the buses and trains stretch out into the suburbs so it's not very hard to travel around on public transport. The free travel is aimed at reducing the traffic at the centre so using your hire car to take you into the busiest areas might be a little stressful, and taxis can often be hard to come by so make sure you plan your journeys in advance. There are plenty of cycle routes and lots of pedestrianised areas so Perth is a great place to kickstart that exercise regime and do some sightseeing at the same time.
Domestic flights are the best way to travel vast distances in Australia but if you prefer a slower pace of life there are plenty of options. You could drive the coastal road from Perth to Melbourne and take in some of the most dramatic coastline you could ever hope to find, but be warned, it's not a short trip! With your hire car you could also head north to the Coral Bay area of the state to combine your city trip with some great diving. Alternatively embark on one of the world's greatest train journeys from Perth to Sydney via Kalgoorlie, Adelaide and Broken Hill. You can also head up to Darwin or Broome on the greyhound coach but this trip is also not for the faint of heart or the easily bored!