Reading values from an Analog flowmeter

Hardware, SIEMENS S7-224XP cpu and a Flow meter (analog)

I am trying to understand if using a DIGITAL flowmeter would be easier (and economical) or an ANALOG one?

particularly, I am not sure how conveniently the averaging of the flow meter values can be done,

For instance a F/M gives a value X1 for duration T1, X2 for T2, X3 for T3, and so on....

I understand how it is to be totalled, but to do it quickly and accurately, since I've never done such an application, I would appreciate all the help I can get.

Thanks

Analog for flow is fine in most cases, you shouldn't need to average , just apply some damping to the meters analog output.
I think you are asking about intergration, the easy way is to take the flow every few seconds, divide it by your frequency and add it to a register,
For example you have a flowmeter that measures in liters per minute. (for this example the flow is 30 liters per minute)
Every 6 seconds take the flow rate (30) divide by 10 and add it to your accumulator
After 6 seconds it will read 3.0, 12 seconds 6.0, 18 seconds 9.0 ------ 60 seconds 30.0
I always use 6 seconds because it divides by 10 but there's no reason why you couldn't use 5 and divide by 12
Of course if your flow meter is in liters per hour every 6 seconds you would divide by 600 and add to the accumulator.
If your PLC has a real time clock use that rather than just a regular timer.
Hope this helps
Roy