Which form to use for the application itself depends on the size of the estate (small or regular) and whether there is or is not a Will.
When you file an application you must include a properly prepared draft Order which when issued constitutes the Certificate of Appointment of Estate Trustee. It needs to be complete and ready for signature by the Court. If there is a Will, the entire Will must be included with the Order.
When there is a Will, the applicant must establish that it was signed by the testator. Normally this involves using an "affidavit of execution". However, if none is available, then creative lawyering is required to use other means to prove the siganture.
Unless the applicant is the first named exeuctor in the last Will, the applicant must file evidence that they are entitled to be appointed the estate trustee. Depending on the circumstances, this can include death certificates, divorce Orders, renuncatiations and consents from the applicable people. For intestacies, signed consents of beneficiaries entitled to .50% of the estate are required.
Before it is filed with the Court the applicant must have been served properly on the right people the proper time in advance. Who requires service and in what form depends on the nature of the beneficiaries. Especially important is dealing with service if any of the beneficiaries are under 18 or incapable of managing their own finances.
Unless the applicant is an executor named in the Will, the applicant must deal with the issue of 'bonding' either by posting a bond or surety, or, by applying for a Court order to dispense with the requirement to post a bond. Neither of these options is easy or straigthforward. Dispensing with a bond requires, among other things, 100% consent of the beneficiaries.
Applicants must calculate and submit payment of the entire estate administration tax when their application is filed with the Court. Often applicants require assistance getting this payment from the funds of the deceased. It is possible in some circumstances to request an Order permitting deferred payment - this is not straightforward.