As a British citizen, you are eligible to obtain an ETA through a travel agent, airline or Australian visa office providing it is outside Australia. It is a very simple process and is relatively simple to complete the form. Once it is issued there will be nothing placed in your passport. As indicated it is completely electronic. If you are just visiting family and friends or as a tourist this is the best option.
The Working Holiday visa is for those that would like to visit Australia but need to do casual work along the way to supplement the holiday. The United Kingdom is a participating country. The catch is that you must be under 18 but not older than the age of 31. You may work for a maximum of six months at any one job, but the visa is good for 12-month intervals without having to leave and re-enter. Like the ETA, this visa must be obtained prior to arriving in Australia unless it is a renewal, which can be done while in the country.
You must be registered for full-time study at an approved institution to qualify for a student visa; however, you will be able to bring family members along with you. As an undergraduate, you or your family members will be permitted to work no more than 20 hours per week. If you are a master's or doctoral student there is no limitation.
Australia recognizes same-sex partnerships, fiances and those already married as eligible for a resident visa as long as the partner is an Australian citizen. This visa should be requested prior to entering, but can be applied for once in the country as well. Temporary status will be granted for two years from the date of application followed by permanent status. Both entitle the bearer to work and study, but only the permanent status qualifies the new resident for Social Security and government medical care.
Australia is always looking for skilled workers to emigrate. Their needs change often so it is best to check frequently if considering a move from the U.K. to Australia. There is a directory called the Migration Occupations in Demand List (MODL) that is updated regularly. The categories range from management to professionals to trades. The process for this type of visa is complicated, but it can be made simpler if you already have an offer from an employer.