Do you think there are songs that ought to be learned first, songs that give the best foundation for further study? There are certainly songs that seem hard enough that they would have to be left for last...
Your questions are obviously vast but here are a couple quick thoughts. I wrote this a while ago for totally different reasons but I think it applies to your question.
Sunshine DayDream, Throwing Stones, Althea, Deal, etc. are NOT huge jam songs. They aren't "little tunes", but aren't HUGE jams either. Like, say Stella Blue or Eyes Of The World, they are longer songs with a structured jam in them that generally stays withing the confines of the chord changes.
I will say there are some songs that kinda fit in between because they tend to jam over a single chord but, they generally stay pretty tied in to the groove of the song and generally do not reach psychedelic heights of any serious magnitude. Shakedown Street is an example as is Crazy Fingers, Here Comes Sunshine, and others. I can even give you the benifit of the doubt and say these are Quasi-Huge Jam songs.
There are only a dozen or so "HUGE JAMS". These are when they opened the "Tripping Doors".
These include Bird Song, Cassidy, Estimated Prophet, Dark Star, Slipknot!, Supplication, the F Part of Terrapin Station, Jam after Terrapin Station ('90), Music Never Stopped, Playing In The Band, occasionally Not Fade Away (only the sickest versions apply), and sick, long segues between songs like Scarlet Begonias > Fire On The Mountain or Lost Sailor >Saint Of Circumstance.
My overly simplified view is that the GD have small tunes, big tunes and Huge-Jam tunes.
Some small tunes to learn first IMHO would be ones like Friend of the Devil, Bertha, Franklin's Tower, Cold Rain and Snow, as well as all the blues-based tunes as they're a bit easier to deal with.
Big tunes to look at next might be ones like Shakedown Street, Eyes, The Other One and Wharf Rat to name a few. Tunes that I'm calling "Huge-Jams" are also worth getting into right away as the biggest "part" about playing them is improvisation over the changes/chord structure.
Also, I think it's most common to "break-down" the various periods based on the members of the band. So, you have (basically) the Pig era, Keith and Donna era, Brent era, post-Brent and post Jerry incarnations. Hope that helps a little and welcome to RUKind.