Before both. The review is worth completing before you accept the employment contract and before the online application fee is paid, because the gift itself is made only later, after successful vetting and when you are instructed. Reviewing terms after money has moved narrows your options considerably.
Sequencing the review, the payments and any right to work
Official descriptions of processing in weeks are descriptions, not guarantees, and a qualified estimate on your own file is more useful than a blanket refusal to estimate. Do not treat a paid fee, a filed case or a funding approval as permission to work or as residence; work before residence depends on separate, valid authorisation you already hold. Residence itself generally authorises employment on admission.
Where the framework is genuinely being pursued, build the schedule around confirming current terms close to the date of any commitment, because the conditions of a recent programme may be adjusted between the day a plan is made and the day funds move. The processing fee is paid first and is nonrefundable, vetting follows, and the gift comes after vetting rather than before it, so the funds are not all needed at the same moment.