Hello Goldsmith,
80W at 3 MHz is certainly possible with cheap (switch mode) semiconductors. The capacitors will probably be the most expensive components.
In case of low supply voltage, push-pull circuits are attractive (tuned Royer or Baxandall oscillator all with center tapped transformer or resonant circuit). The tuning capacitor avoids the need for a transformer with low leakage inductance. Even a center tapped LC circuit without magnetic core does the job. Drain voltage is about 3.3*supply voltage. Both semiconductors are at same potential (ground).
You need some Q factor in the resonant circuit. At 3 MHz you need good capacitors. The problem in this type of oscillator is that you need good 50% duty cycle, otherwise the efficiency drops and/or you get smoke. So you need a form of bias setting feedback that maintains 50% duty cycle. With BJT the BC junction can be used for that, but with mosfet/IGBT this doesn't work. Advantage of the resonant push-pull oscillators is that these oscillators are not load critical (they even run without any load).
When the tuning capacitor is split in two capacitors (each capacitor goes from drain to ground), you will get a balanced class E oscillator. Main disadvantage is that even under no-load situation, all oscillating current goes through the mosfet and the body diode, of course this is no problem when the oscillator runs with nominal load only. Note that not all mosfets have fast enough body diodes for operation at 3 MHz. Main advantage is that the duty cycle isn't very critical.
When running from high supply voltage (where silicon mosfet properties are not that good anymore), the half or full bridge oscillators are best, as the drain voltage equals the supply voltage. Also here you can have zero voltage/current switching reducing the switching loss to a negligible value (with respect to conduction loss). There exists a so-called current fed half bridge oscillator circuit, but I have no experience with it.
Older CFL or TL use (for example) a voltage fed half or full bridge oscillator directly fed from rectified/filtered AC mains. Most of them are (quasi) resonant to reduce switching loss and setting the frequency. Most modern types use additional control now (dedicated chip or microcontroller).
For all oscillators: you should evaluate the turn-on behavior and behavior under non-optimal load. Several oscillators require a certain minimum load, or can't accept too heavy load. Depending on the bias circuit, you may need a starting pulse (in older electronic ballasts frequenly generated with a diac).
Many oscillators will not work well when followed by a filter (for example to suppress harmonics). It may oscillate on some other (parasitic) circuit resonance.
If you need high efficiency in the low MHz range from low supply voltage (using mosfets), I would not go for a true class C approach.