As a keyboard player -
- yes, inversions are super easy - all we do is not play the root of the chord as the lowest note in our LH.
Some examples -
C/E = E G C
D7/F# = F# A C D
and we can rearrange the notes in our RH, too.
As a guitarist, IMO you don't really have to worry about the letter after the slash (although the Bass player does, that's what they should play)
The other kinds of slash chords are -
what I call 'passing' (like C/Bb in a C, C/Bb, Am progression). Usually play the chord before the slash.
and the Jazz-type chords (maj/min/sus/dim/aug 9ths, 11ths, 13ths). These have more than four notes, and are often notated like -
C/D - can be a Dsus11, D C E G, - or - D F A C E G
D/C - most likely some kind of a C13th(#11) chord = C E G Bb D F# A
Often we notate them this way out of habit, or because it's easier to think, "LH - C E G, RH - D F# A" . Notice the Bb got left out. Or I might play - LH - E Bb RH - D F# A, leaving out the root (C).
Very common to leave out notes w/jazz chords - and players often do, or stack them in 4ths, for a jazzier sound. You can, too. I'm not sure, but in my experience have seen jazz guitarists voice these chords higher than the standard C, G, D, A, E triads.
chord symbols - can be an inexact science...