I agree with all the Cure and Smiths recommendations, it sounds like like stuff would be up your alley.
I've some more "proto-punk" (i.e. precursors to punk) and 80s "post-punk" for you. (not in any particular order) Descriptions to follow.
1. The Stooges - (self-titled)
Undeniable. Once you get into this, there's no turning back. I guess they're considered "protopunk" but it's kind of a silly label. They stand on their own. (Check out the obvious Stooges influence on Echo & the Bunnymen on some of the songs Ocean Rain)
2. Modern Lovers - (self-titled)
[img][250:250]http://upload.wikimedia.org/wikipedia/en/0/00/Modernlovers.jpg[/img]
Amazing protopunk record. Jonathan Richman is an amazing songwriter.
3.Tones on Tail - Everthing
The intermediate stage between Bauhaus and Love & Rockets. This complilation is what it says it is: everything they ever put out. It goes from fun new wave hits like "Go!" to weird-ass spacey dark jazzy stuff.
4. Echo and the Bunnymen - Ocean Rain
[img][250:250]http://perso.orange.fr/religionnaire/artistes/80s/art/ocean_rain.jpg[/img]
A beautiful album. They have many good ones. I listed this becuase it's good all-round and includes "The Kiling Moon".
5. The Cure - Standing on a Beach
A compilation of their early stuff. Includes clasic stuff like "Close To Me" and "Inbetween Days". But buy Disintegration first.
6. Siouxsie and the Banshees - Juju (or just get one of the compilations)
[img][250:250]http://www.vamp.org/Siouxsie/Images/album-juju.jpg[/img]
Severely underated band from the 80s. They grew out of the 70s scene and then took their music in bzarre and original directions, (Robert Smith from the Cure was briefly a member). This is a good record, but you could also do well with the compilation "Twice upon a time".
7. The Smiths - Louder Than Bombs
[img][250:250]http://static.last.fm/coverart/300x300/1414109.gif[/img]
Yes, it's a compliation, but a lot of Smiths records incorporate stiff frmo their other records. Apart from The Queen is Dead, this is probably the best intro to them.
8. Depeche Mode - Music for the Masses or Violator
[img][250:250]http://www.caltechgirlsworld.mu.nu/archives/images/Depeche-Mode-Music-For-The-Masses.jpg[/img][img][250:250]http://www.depechemode.se/Albums/images/violator_large.jpg[/img]
These guys have lots of records. The earlier ones are closer to "80s synth pop" and the later ones get a little different too. I picked these because I consider them to be their most seminal work.
Oh, in terms of 60s psych-garage you should definitely pick up this:
(it's on rhino)
That's all for now, but feel free to ask for further suggestions or descriptions. I love posting this kind of stuff.
Note: Artistis like The Cure, Siouxsie and Depeche Mode all have many albums, most of which are good. I just picked ones that I feel are good intro albums or good "surveys" of their stuff.