Should I start with the movie from '88 or first watch the series completely and then the movies, or what? Is the series the continuation of the movie from '88, or is it like GITS:SAC which is an alternate story? Help!
The Angels have the Phonebox
Exclude side story (Golden Wing & others), the first thing to watch should be "My Conquest is the Sea of Stars", which is where Yang and Reinhard first encounter each other in battle. Then, "Overture to a New War" which actually over lapse the first 4 episodes somewhat, and then the OAV, starting at episode 1.
The side story OAV deals with the main character when they got started in their careers.
Here’s the chronological order of the ever-growing number of anime films and tv series:
Spiral Labyrinth (Gaiden 2, episodes 1-14)
Silver-White Valley (Gaiden 1, episodes 1-4)
The Mutineer (G2, ep. 15-18)
The Duelist (G2, ep. 19-22)
Golden Wings
The Retriever (G2, ep. 23-26)
Dream of the Morning, Song of Night (G1, ep. 5-8)
A Hundred Billion Stars, a Hundred Billion Lights (G1, ep. 13-24)
The Third Tiamat Battle (G2, ep. 27-28)
My Conquest is the Sea of Stars
Disgrace (G1, ep. 9-12)
Overture to a New War (an expanded retelling of the first two episodes of the main OVA series)
Main OVA series (this 110 episode series)
Source: https://en.wikipedia.org/wiki/List_of_Legend_of_the_Galactic_Heroes_episodes