The most common mistake is promising resolution times before you know your own numbers. Start narrow, then tighten.
A first response target is one you control. A resolution target depends on how hard the problem turns out to be, and a small team that misses it repeatedly stops trusting the metric. Switch off resolve within on the policy, run for a month, then add resolution targets once you can see what is realistic.
The default policy is 4 hours across the board, which is a reasonable place to start if you would rather not split by priority yet.
Use operating hours rather than calendar hours, or a ticket that arrives at 11pm burns most of its target before anyone is awake. Add your public holidays so a closed day never counts as a breach. This single setting is the difference between a metric people trust and one they argue with.
When you are waiting on the customer or a supplier, move the ticket to a pending status so the clock stops. That is not gaming the number - it measures the time you actually controlled. It only works if the team applies it consistently.
Four levels is enough for a small team. Reserve Urgent for work that has genuinely stopped, or within a month everything will be urgent and the priority will mean nothing.
Choose a reminder interval and nominate who gets alerted. Being told half an hour before a target is missed is useful. Being told afterwards is just reporting.