One thing to consider is that his works have varied in content, style, and genius over the years, such that each "era" might have a different list.
Not an attempt to answer that question, but I wonder who picked the songs on the 1994 "Best of Daniel Johnston" CD called "Please Don't Feed the Ego".
They are (with my comments)
01 Speeding Motorcycle - yes, certainly
02 Sad Sac + Tarzan - yes
03 Impossible Love - yes
04 Casper the Friendly Ghost - yes, certainly
05 Come See Me Tonight - very good song, but not normally considered one of his genius works - still it appeals to general idea of what a song is and should be
06 Funeral Home - definitely powerful - may be hard for a newcomer to appreciate
07 Since I Lost My Tooth - no opinion
08 Don't Play Cards with Satan - yes - powerful
09 Big Big World (w/ Rhythm Rats) - this one surprised me - this IS a very very good song - but very different - very "polished" production for Daniel - still, not normally held out as one of his big ones - but it has an appeal
10 Bloody Rainbow - yes
11 More Dead Than Alive - no opinion
12 Joy Without Pleasure - no opinion
13 Fly Eye - no opinion
14 My Life Is Starting Over - yes - very Daniel Johnston
15 Running Water - wildly original and genius - but again, may be hard for a newcomer to appreciate
16 The Story Of An Artist - undecided
17 Walking the Cow - certainly a well received song
18 I Killed the Monster - highly representative of his honesty and depression
19 Casper The Friendly Ghost #2 -

20 Rock 'n' Roll / ega - "yes" - this is also very very different - and used in the movie "The Majestic" -