Fortunately for us, a dedicated ham has done the math and published a guide for ideal power levels and proper output filters.
John Andrews, W1TAG tells us "...we need to deliver 4.6 milliwatts to a half-wave dipole, or 2.3 milliwatts to a quarterwave ground plane antenna. That’s not much power, but it should be easy to generate."
So how would we know? Fortunately, W1TAG has the answer. "At 50 Ohms, 4.6mw represents 0.48Vrms (1.36Vp-p), and 2.3mw represents 0.34Vrms (0.96Vp-p)."
W1TAG wraps up his great article with some RF clean up advice. "The out-of-band and harmonic suppression requirements are a bit tight... I would suggest a 2-section half-wave filter at the 50 ohm transmitter output..." and the assembly instructions and schematic ar provided in W1TAG's comprehensive article.
But wait, there's more!
You can read the full article at W1TAG's website at http://www.w1tag.com/Hifer2.pdf and be sure to check out his LoFer work, if you are so inclined.
There's lots of bandwidth out there for experimentation, so do some!