What's the best way to install permanent high/low gauges in a compressor based HVAC system rfc134a?
You would not want to install a gauge set with flex lines on your system.
Why would I say this ? They will leak over time.  The larger line with the service port is the suction line. I have a “low pressure” gauge with a flair fitting that is only ~1” long for checking system pressures.  I attach the gauge and open the valve verify operational range and close the valve.
Why would I not leave a gauge on that port? The ports when open have a higher chance of leaking not only at the flair fitting but at the valve. Notice the threads on the valves over the hex valve fitting? Those need to be capped that location is the #1 location I find leaks I use a thread sealant and always close those off.
As far as the size there are 2 normal sizes 1/4 flair and 5/16 flair  these fittings are not standard flair fittings as they have a valve stem depressor that opens the Schrader valve. If installing gauges on systems was a good idea mfg’s would have this as an option (they used to install sight glasses) but since sight glasses and gauges tend to be a leakage point they are not an option (or I am not aware of a residential system with gauges as an option). I would use caution in even checking the low pressure of your water heater if similar to mine it only uses 3/4lb of r134 each time the system is opened a small amount of the charge is lost this is why I have the gauges with 1” connections. Connecting a standard line set to a small system like this several times can loose enough of a charge to cause problems due to low charge.
Last the EPA can levy fines for a non certified person for opening a system would they for checking your system?  I don’t know of that happening but you could damage your system or introduce leaks by moving forward.