As it turns out both current flow, and electron flow, are equally valid in a practical sense, until you get to the point where you are trying to understand things like vacuum tubes, solid state physics, or electro-chemistry, where you are actually trying to deal with electrons.

In the top pictorial, I show the simplest of circuits. Electricity flows from one end of the battery, through the resistor, and back to the other end of the battery. If you're a "current flow man" (sorry ladies but I have never heard that vernacular used in the female context, and to do so here I feel would be demeaning of the female gender), any way if you're a "current flow man" the blue arrow at the top, depicts the current flowing from the (+) positive terminal of the battery, through the resistor and ultimately completing the circuit as in enters the negative end of the battery. If on the other hand you're an "electron flow man" to you the world is upside down, electrons flow from the (-) negative end of the battery, back up through the resistor, and back into the positive end of the battery. Both notions are equally valid. Select one, as your primary method of conceptualizing a circuit, and fall back on the other, for deeper understanding.

At the risk of alienating many authors of text books on this subject, Electrons do not really flow through wires. What happens is, a charge disturbance, such as an electric field, AKA "a potential difference" enters a conductor at one end, applying electrons to the loosely bound electrons in orbitals of atoms that make up the conductor, by providing "Extra" electrons some of these find their way into a weakly bound orbital. The extra charge they carry, makes the atoms orbital unstable, and so it gives up it's own electron, part of the time. That electron does the same to another atoms, whose location in the conductor, is less likely to compete with the general charge entering from the end causing the disturbance in charge

Incidentally the difference between a conductor, and a non conductor, is the lack, of any loosely bound electrons. In a non conductor, an "insulator" all of the electrons are tightly held in place, by stable charge pairing. Resistors, and semiconductors live in a grey area, between having really easily dislodge-able electrons, and tightly held electrons.

A first order approximation of a wire, is that all points along the length of the wire are a single point, an Ammeter tries real hard to be a wire, that is, if it is a good Ammeter, it is a good approximation of a wire. To be a good approximation of a wire, it needs to offer as little electrical resistance as possible. The reality of this is that in order for current to move the pointer needle across the scale, some electrical energy must be extracted from the system. Therefore a real Ammeter has, unfortunately, some electrical resistance. A Volt Meter on the other hand, if it is a good Volt Meter, should be an open circuit, that is, it should be of infinite resistance, however the reality of energy being required to push the pointer indicator needle across the scale, makes this lofty goal impossible. Real Volt Meters have less than infinite resistance, they infact do draw some, small amount of current.