There are lots and lots of options nowadays for recording your parkrun, and the prices vary enormously. Even within the Garmin stable you could pay from under £50 for a fully working second-hand unit, to £500 or more for the latest and greatest. All devices offer the same basic functionality (most importantly, GPS and heart-rate recording), so what really is needed for the parkrun?
GPS, despite being well established and reliable, is ever-improving. Handheld devices also keep getting better at making sense of the GPS signals being beamed from the satellites. The big problem with parkruns is that the distance you record can be cut short because all of those corners you take get cut off a little bit. The upshot of this is that your 5km run will end up being only 4.95km by the time you see it on Strava, so won't actually count as a 5km run! There are two ways to limit this; using more types of GPS networks does help (eg, GLONASS), but the most significant improver (in the Garmin world anyway) is to use one-second recording.
The point of one-second recording is that lots more location points will be collected for your run. The standard method that Garmin units use is "smart recording", where points are only collected when deemed necessary. Smart recording is fine for cycling and long-distance runs, but not for running around a park. Not all Garmin devices support one-second recording, so make sure that you investigate any device's capabilities before purchasing.
For example, the Forerunner 55 does support the more accurate 1-sec recording mode, but its predecessors (the 45 and 35) don't. Also, the Garmin Instinct (a current model as of 2022) does not support it. The Forerunner 230, 235 and 245 all do have the 1-second recording option.