Paul H
As a new PPL you fly quite well. The landing in particular was nice with no porposing in the flare and a nice tail low touchdown.
You asked for some construcive criticism so here is my thoughts (I am an experienced instructor)
1) I second the above comments on the checklist. You have a good flow and obviously have worked at and are comfortable with the checks, but you should still "check" your actions once completed with the "checklist". Memorized checks for inflight busy periods like in the circuit are entirely appropriate but when the aircraft is not moving like pre/post start and pretakeoff you should use the checklist.
2) Get set up with seat belts on, seat adjusted cockpit organized before you start the engine. I strongly recommend the shoulder belts be used. If you crash with only a lap belt your head will impact the middle of the instrument panel. Imagine how your face will look after it smashes into all the knobs and protuberances on the panel.......
3) IMO you are placing excesive faith in the parking brake. The aircraft was pointed at a open hangar and was running while you were head down fiddling with the seat, closing he storm window, etc etc. Piper park brakes are not too bad but the Cessna ones (and many other light aircraft) are generally terrrible. It is a good idea to expect the park brake to slip and therefore keep an eye outside any time the engine is running
4) Do one task at a time. As you get more experience you can multitask, but as a new pilot give yourself some extra margin. So for example when starting the engine all you attention should be on that task and you only move onto the next one when the engine is running smoothly and the after start memory checks (RPM set, oil pressure rising, and ammeter not indicating massive discharge {a sure sign of a hung starter}) are complete.
5) I like to squeeze on a little brake just as the aircraft starts to roll as you start the taxi to make sure the brakes are in fact working, and require even pedal pressure.
6) When doing the runup don't rush. When you checked the carb heat it was only on for 2 or 3 seconds. Remember you are checking 2 things, 1: is the carb heat working and 2: is there carb ice ?. There is no way you will detect both in this brief time. Leave the heat on for at least 15 seconds while minitoring the RPM (you should see the intial drop in RPM indicating that the carb heat is functioning and then a rise in RPM if ice were present. If a lot of ice is present the engine will intially run rough which is a positive indication of ice build up but a small amount of ice will only be noticable as a gradual rise in RPM as it is melted off). For the mixture check I like to do it immediately after the carb ice check with the carb heat still on. As the mixture is slowly leaned the RPM should slowly rise as the overly rich mixture created by the carb heat is reduced and then the RPM should drop as the mixture becomes overly lean. This is a very good check that the mixture control is working properly and that the carburator is properly set up.
7) For most emergencies there is no rush to complete the vital actions, The main exception is the takeoff engine failure/fire senario. I teach that the last part of the pretakeoff check is to verbalize the actions that will be taken for an engine failure during the takeoff and for an engine failure after takeoff. This mental preparation primes the brain for the quick actions that are required if the worst happens.
8) I also like to use one hand on the stick and one hand on the throttle for takeoff. The control forces are not high so there is no reason not to guard the throttle on takeoff (and landing too).
9) I want my students to verbalize what I call the "good engine" call on takeoff. As soon as the trottle is fully advanced they look at the RPM guage and verify that the engine RPM is within the static RPM limits and that the main engine gauges are in the green.
10) IMO your flap retraction after takeoff was unnecessarily delayed. The purpose of the flaps is to help get the aircraft off the ground. Once it is off and climbing solidly at the Vy and clear of obstactles retract the flaps to maximise rate of climb. Altitude is your friend, you want to getthat first 1000 feet as quickly as possible.
It is easy to nit pick a video from the comfort of your computer screen so please do not take the above as me throwing rocks at your efforts. There is also more than one "right" way to fly an aircraft. My comments were meant to give you some things to think about and of course should be compared/contrasted with other opinions
Have fun flying !