Yeah it's an 8ohm speaker.
Since my original post I've come to the conclusion I need two separate amplifiers. One to take very small voltages to line level and an audio amplifier to take line level up to power a modest speaker.
The former will be in a metal project box for shielding with BNC connectors
I think you've discovered that opamps have limited output power - they can only provide so much current, and speakers can take a fair bit of current, and also they're an inductive load. 'Small-signal' amplifiers do not require high power outputs - they are there to amplify, attenuate an input voltage, not 'drive' anything. Speaker amplifiers are power amplifiers, whilst they can amplify the input signal their main job is to take an input voltage and 'power' the speaker with an output stage that can provide more than a few mA. Power amps can have a gain of 1, so the output signal is the same level as input, the difference being it can take a weak signal as a reference, and have enough current output to power things from it, namely speakers. (not the best explanation!)
I think you should google for introduction to opamps. Operation amplifiers have many properties, and for students it can be fruitful to understand the 'ideal opamp', and then find out what makes real-world opamps non-ideal.
The difference between a 'single supply' opamp and a 'dual supply' isn't so much about how the opamp operates, but rather the limitations of its inputs and outputs. Some opamps cannot sense inputs close to its power rails, others can sense down to their Negative rail, but only within 1.5-2V of its positive rail. It is a similar deal with outputs.
The LM324 is the quad version of the LM358, whose inputs and output can reach '0V' (note, this is the negative rail of the opamp, not necessarily 0V in circuit!) but cannot output voltages higher than its positive rail - ~1.5V. It can be called a 'single supply' opamp, because you can hook its negative power rail to 0V, and positive to say, 5V, then any AC waveform on the input should be biased to above the negative rail - otherwise the negative side of the AC waveform will go below 0V (its negative rail) and so, cannot be sensed. The output similarly, can go from 0V to ~3.5V. So the system only requires a single 5V power supply, but its input and output can only go between 0 and 3.5V and so any AC waveform has to be biased in-between these so it can go above and below this bias point, say 1V to 3V, baised at 2V.
Other opamps can have their inputs/outputs hit (or get very close to) the positive rail, but only within 2V of the negative. And then there are 'rail-to-rail' opamps, where either the inputs, or outputs, or both, can get quite close to the power rails - handy for battery powered applications where its powered by lower voltage, say 3V. Often these are specifically designed for low voltage (max power voltage 5-12V), where-as opamps that have IO that can only get within ~2V of either power rail, can operate from +/- 15V supplies.
Dual supplies can greatly simplify matters as everything is referenced to 0V/GND. In 'single supply' opamp circuits, everything is referenced to a 'virtual ground' - a biased point somewhere between the power rails, often VCC/2. For Audio, which of course is all AC, having dual rails makes life easier. If you used a single supply to power a speaker (very common) then the output 'sits' at half the power supply voltage, so to drive a speaker, one uses a fairly large output capacitor to block this DC bias - so it sits at 0V/GND.
I'm just rambling now, food for thought?