I consider a passenger safety brief as outlined excellently by poss to be separate from a Captain's brief.
The purpose of a Captain's brief is, as a PPL, to brief YOURSELF (and any instructor/examiner/other PPL who might be flying with you) about what you are going to do, with emphasis on what is different for today from any other flight. You need to cover speeds, power settings, emergency actions as always, but include weather - wind, runway state (surface grass/concrete, dry, damp/wet), cloud, anything in THIS aircraft which might be different from others, etc.
Hence I encourage sudents to say something like
"We will be taking off on 25. The wind is southerly, so at the start of the ground roll I will hold a bit of into wind aileron and reduce as we gather speed. After applying power I will check full power is developing, temperatures and pressures in the green and steady, and airspeed rising. Keeping straight with rudder, I will be taking pressure off the nosewheel at 50 knots, commencing the rotate at 55, and getting airborne at 60, with a slight pitch forward to increase speed to best climb speed of 65 kts, at which we will climb out and, after reaching a safe altitude, take up a heading of nnn degrees.
The runway surface is dry, so no braking action problems today. In the event of any problem occurring on the runway, I will cut the power and apply braking, vacating the runway if necessary (and possible) and carry out further actions as required. In case of a serious problem and if we are already airborne and there is sufficient runway remaining, I will land back on and apply up to maximum braking, further actions as dictated by the nature of the problem. If there is no runway remaining and an immediate reland is necessary, I will look for a suitable clear area either side of the nose, favouring out to the left as that is where the wind is coming from today. In case of an emergency that doesn't require an immediate reland, I will declare an emergency, carry out a visual circuit and land back on 25.
Any questions or comments?"
The purpose, as I say, is to brief yourself. Imagine you are briefing someone else, and hopefully you may cover something that you had not up till that point, thought of.
The main briefing point, of course, is ensure your safety. Second point is ENJOY IT. If you don't enjoy it, there's no point in doing it.