What is the most simple plane lift equation that gives realistic solutions?
First, you need to add the effect of density $\rho$: Air density changes with altitude, and this affects both lift and drag (at least if you model airbreathing engines).

For lift $L$, use $$L = c_L\cdot\rho\cdot\frac{v_h^2+v_v^2}{2}\cdot S$$

For drag $D$, you should only simplify the equation as much as possible. Your equation is simpler still and doesn't model the increase in drag with more lift. The simplest practical equation will look like this: $$D = \left(c_{D0} + \frac{c_L^2}{\pi\cdot AR\cdot\epsilon}\right)\cdot\rho\cdot\frac{v_h^2+v_v^2}{2}\cdot S$$

More lift will need more thrust and will limit the upward acceleration. Climbing higher will reduce thrust in proportion with density and limit the possible speed range.

Nomenclature:
    $c_L \:\:\:$ lift coefficient (normally between 0 and 1.5)
    $\pi \:\:\:\:\:$  3.14159$\dots$
    $AR \:\:$  aspect ratio of the wing (ratio of span to mean chord)
    $\epsilon \:\:\:\:\:$  the wing's Oswald factor (use 0.8 when in doubt)
    $c_{D0} \:$  zero-lift drag coefficient (use 0.02 when in doubt)