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For any of these starting positions, GEO, GTO, EM-L2 or EM-L4/5, which would require the least delta-V to get to Sun-Earth L1? How much delta-V would it require?
Would this chart help in identifying which delta-V would most likely fit the requirements stated?
$\rm L_1$ is a similarly circular orbit, and according to this source, the Earth-Sun $\rm L_1$ is $\approx$ 1.5million km from the Earth. Between circular orbits, the cheapest transfer is the Hohman transfer.
According to the Wiki page, the required $\Delta v$ for Hohman-transfer orbits is
$\Delta v = \sqrt{\frac{\mu}{r_1}} \left( \sqrt{\frac{2 r_2}{r_1+r_2}} - 1 \right) + \sqrt{\frac{\mu}{r_2}} \left(1 - \sqrt{\frac{2 r_1}{r_1+r_2}}\right)$
Where $\mu$ is the "gravitational parameter" ($\rm GM$, the mass of the central body multiplied with the gravitational constant), and $r_1$, $r_2$ are the radii.
Although this formula could be significantly simplified using that now $r_1 \approx r_2$, substituting the values ($M=2\cdot 10^{30} \rm kg$, $r_1=1.5\cdot 10^{11} \rm m$, $r_2=1.515\cdot 10^{11} \rm m$, $G=6.67\cdot 10^{-11} \frac{\rm Nm^2}{\rm kg^2}$), we can get the required $\Delta v$, which is $\approx 148 \frac{\rm m}{\rm s}$. This adds to the escape speed from the Earth ($\approx 11.2 \frac{\rm km}{\rm s}$) or from LEO ($\approx 3.4 \frac{\rm km}{\rm s}$).
