Your base idle speed has to be done on a fully warmed up engine and those specs should be listed on the underhood sticker.
There is also an AC idle speed to bring the idle up whenever the defroster or AC are running.
In a high mileage engine, there may be some roughness to the idle due to wear, vacuum leak(s) or bad motor mount(s).
Your vacuum leak may not be an obvious one.
A sticky PCV valve (pinch the hose and, if the idle smooths out, change the PCV valve) or a leaking brake vacuum booster (again, pinch the hoseoff to see if idle smooths or intake manifold gasket leaks are less obvious but just as detrimental.
A sticking EGR valve will also be a less than apparent vacuum leak.
Not sure if Hondas are picky and must have a genuine Honda brand PCV or not.
You mention the idle speed being too low in the AM when the car is first started.
No idea what your experience is with carbureted engines, so I wondered if you’re aware that carbureted cars require that you fully depress and release the gas pedal before starting in order to engage the fast idle cam.
By design, the fast idle will not disengage until after the throttle is moved/gas pedal is depressed.
2000-3000 RPMs at startup is the range for the fast idle speed.
It will then drop in 500RPM increments until it is off the fast idle and onto the idle circuit.
This relies upon a good working electric choke and a working thermal vacuum valve, as well as a proper fast idle adjustment.
Assuming your mechanic adjusted the idle mixture screws properly, there’s an easier to follow link (than the idle mix link) for the base idle speed adjustments.
There are many adjustment screws on these carbs, so you have to be absolutely sure you’re turning the right one beforehand.
It’s the one closer to the firewall with a plastic cap/knob on it.
Since the quality of a rebuilt carburetor depends on the rebuilder, know that a bent idle speed screw will wreak havoc with the idle circuit.
This page details the exact procedures for idle adjustments but you must follow them to a T.
http://www.autozone.com/repairguides/Honda-Accord-Prelude-1984-1995-Repair-Guide/IDLE-SPEED-AND-MIXTURE-ADJUSTMENTS/Idle-Speed/_/P-0900c1528005f388
When it states that the upper vacuum hose of the idle control solenoid valve has to be disconnected and plugged before adjusting the idle speed screw, then you must do it that way.
Don’t forget to adjust the AC idle speed, assuming your car has air conditioning.