Ranking All 29 Billboard #1 Hits- 1987. A pretty weak year for #1’s overall.
29-‘Shakedown’- Bob Seger
28- ‘Alone’- Heart
27-‘Lost In Emotion’- Lisa Lisa and Cult Jam
26-‘I Think We’re Alone Now’- Tiffany
25-‘At This Moment’- Billy Vera and The Beaters
24- ‘Nothing’s Gonna Stop Us Now’- Starship
23-‘Livin’ On A Prayer’- Bon Jovi
22-‘I Knew You Were Waiting [For Me]- Aretha Franklin and George Michael
21-‘Always’- Atlantic Starr
20-‘Here I Go Again’- Whitesnake
19-‘Ive Had The Time Of My Life- Bill Medley and Jennifer Warnes
18-‘Didn’t We Almost Have It All’- Whitney Houston
17-‘Head To Toe’- Lisa Lisa and Cult Jam
16-‘You Keep Me Hangin’ On’- Kim Wilde
15-‘Lean On Me’ Club Nouveau
14-‘I Just Can’t Stop Loving You’- Michael Jackson with Siedah Garrett
13-”I Want To Dance With Somebody Who Loves Me’- Whitney Houston
12-‘Shake You Down’- Gregory Abbott
11-‘Jacob’s Ladder’- Huey Lewis and The News
10-‘Mony Mony’- Billy Idol
9-‘La Bamba’- Los Lobos
8-”Who’s That Girl’- Madonna
7-‘Bad’ Michael Jackson
6-‘Open Your Heart’- Madonna
5-‘I Just Died In Your Arms’- Cutting Crew
4-‘Heaven Is A Place On Earth’- Belinda Carlisle
3-‘Faith’- George Michael
2-‘With Or Without You’- U2
1-‘ I Still Haven’t Found What I’m Looking For’
slicethelife 
Looking at these tunes now, I used to like many of them more back in the day than I do now.
“The Joshua Tree” is my favorite U2 album, so I agree with your top 2. “Jacob’s Ladder” and “Livin’ on a Prayer” (I know, here we go again! 🙂 ) probably would be in my top 10.
80s music seemed to be a refreshing change from the monotonous music of the prior disco era to me.
Starship needs to be #29 and Tiffany needs to be #28. OY.