Since you haven't supplied much detail, I'll have to use nonspecific examples based on typical installation methods.
Furnace and Condensing unit
If you have a setup where you have a furnace, and an outdoor condensing unit. The wiring will be similar to this (Note: This is a basic overview, not actual wiring).
Basically, the R wire provides power to the thermostat. W, Y and G are energized depending on the state of the thermostat. For example. If the thermostat is set to the COOL mode, and the temperature in the room is above the set point. The Y and G terminals of the thermostat will be energized. This tells the furnace to turn on the blower at high speed, and the condensing unit to turn on. Alternatively, if the thermostat is set to the HEAT mode, and the temperature in the room is below the set point. The W terminal will be energized, which tells the furnace to turn on.
Heat Pump
If you have a heat pump, the wiring will be similar to this.
Here the R wire again provides power to the thermostat. This type of setup uses either an O, B, or O/B terminals to change the state of the reversing valve in the heat pump. In this type of setup, the thermostat works similar to the example above, though it also has to manage an extra terminal.
Some thermostats offer both an O and a B terminal.
When the thermostat is in COOL mode and calls for cool, the O terminal will be energized. If you have a system where the reversing valve is normally in HEAT mode, you'll use the O terminal to move the reversing valve to COOL mode. When the thermostat is in HEAT mode and calls for heat, the B terminal will be energized. If you have a system where the reversing valve is normally in COOL mode, you'll use the B terminal to move the reversing valve to HEAT mode.
Some thermostats offer and O/B terminal, and will have a jumper to select which function it provides.
In this case, you'll set the jumper based on the type of system you have. Then when the thermostat calls for heat or cool, the O/B terminal will be energized appropriately.
For more information on the C terminal, please see this answer.
The test procedure for determining the SEER is quite elaborate, and involves measuring the efficiency at a variety of simulated outdoor temperatures. I'm not sure what the basis for the sales rep's statement was, but without more information (i.e. specific numbers) I wouldn't put too much stock in it. The SEER is not just calculated at a single fixed situation.
As for whether it makes sense, that depends on your climate, the size of the area being cooled, the local price of electricity, etc. I would just use one of those calculators like you've linked to to determine the value, but make sure you get accurate numbers for all the inputs. The cost of electricity varies widely throughout the US, so get a current number for your area in the summer and then maybe round up a bit to account for the gradual rise in prices.
Best Answer
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.