All the above is very good advise according to crunched numbers. 3/4" main long line and 1/2" to 5/8" for the diffuser should work well. I have estimated some differences below.

Assuming the following for the completed setup with 3/4" main line and 1/2" diffuser line and a diffuser at 10 foot deep...

Assumptions...

1.) The pump will put out between 2 - 4 CFM at the diffuser.
2.) Running between 8 and 15 psi.
3.) 0.5 to 1 psi to operate the diffuser
4.) Zero losses for valves and fitting since it is a single pump with a single air line (no constricting fittings or valves).
5.) The diffuser line will be 100 foot long.

Pressure loss through the 3/4" line at the low end of the above pump pressure assumption and the high end of the
CFM assumption from...

https://www.engineeringtoolbox.com/pressure-drop-compressed-air-pipes-d_852.html

yields about 1.7 psi. This is the extra pressure that it takes to push the air through 400 foot of 3/4" line given the best conditions of the assumptions.

Do the same for the 100 foot of 1/2" line...

Yields about 3 psi to total 4.7 psi using the best conditions of the assumptions.

Do the same for the higher end of the pump pressure and lower CFM assumptions and you get...

0.2 psi for the 3/4" line and 0.5 psi for the 1/2" line to total 0.7 psi.

The point of the above exercise is to estimate the back pressure on the pump without knowing the actual numbers, using a range of educated guesses. With the above assumptions and quick calculations...the pump would see a back pressure from the 3/4" and 1/2" lines of 0.7psi to 4.7 psi. Lets use the average for a comparable number for later...2.7 psi.

To summarize, the above mumbo jumbo estimates that the system would have about 2.7 psi of back pressure from the 3/4 and 1/2 hoses alone.

If we do the same thing for 1" line and 5/8" line...we get 0.8 psi

How about 3/4" and 5/8" lines? We get 1.5 psi.

So, you can knock almost 2 psi off the pump by using 1" & 5/8" compared to the 3/4" & 1/2". That's a very nice reduction.

You can knock over 1 psi off the pump by using 3/4" & 5/8" compared to the 3/4" & 1/2". That's a good reduction.

A piston pump is a very good pump style and can put out more pressure than the other options (Rotary vane & Diaphragm) hence producing the CFMs you need without killing the pump. Knocking the pressure requirements down on any compressor pump is a good thing for the life of the pump, however.

Once again, the above mumbo jumbo is just to back up the previous good advise from those that know without having to run some numbers...

3/4" & 1/2" line will work with a piston pump.

3/4" & 5/8" works much better.

1" & 5/8" works even better, but would be overkill, in my opinion, given the extra money that would have to be spent for that last 1 psi. This scenario might prove to be a reuired for a rotary vane or diaphragm pump, but not the rocking piston.