There is a great paper by Fränz and Harper  that describes all the coordinate systems used to describe planetary orbits.
Most of the coordinates that would be relevant to your question are celestial and/or heliographic coordinate systems. The celestial systems use the First Point of Aries as a reference point and then the Earth's mean equator or the equator of date, often for a specific epoch (since the stars tend to move over time). These systems also use the ecliptic plane plane, defined by the orbit of Earth about the sun. They use either a mean ecliptic or one defined at a specific epoch. The heliographic coordinate systems use the solar equator or the ecliptic plane.
I should note the different types of times used and how to reference them, which is actually one of the more difficult parts of these coordinate transformations. There are several times used, including universal coordinated time or UTC, international atomic time or TAI, multiple other universal times, Barycentric Dynamical Time or TDB, and Terrestrial Time or TT.
I say this part is difficult because several of the definitions have changed over time (e.g., UT has had several definitions) and some systems do not have obvious trasformations (e.g., conversion between "political" and astronomical times are not always defined by a nice analytical equation). It is important to get the time correct because the conversion to Julian dates or JD is done with a specific time convention (e.g., J2000 in TDB or TT). The important ephemeris parameters like the mean obliquity of the ecliptic plane are defined relative to J2000 using JD.
Getting the times relative to epochs correct is critical since many of the computations depend upon up to six or more decimal places.