Yeah, sounds more like a question, but I'll end with a request.

I'd been thinking that Complete Works remixes for 4,5,6 were good, but there was nothing complete for 1,2,3. But if any of you had ever heard Rockman Iwao & Rockman Iwao-Ni Side A&B, those arrangements I always thought would have made perfect additions to Complete Works.

But I don't know of any full and complete album arrangements for Megaman 3. So what would be a good compilation, or would one have to just browse many remixes and make an album like that?

If an album does exist, I'd love to hear it.

The direct answer to your question is that Rockman 1-3 complete works basically come from Rockman Power Battles and Rockman Power Fighters, the soundtracks to the two Rockman arcade games (playable on the Anniversary Collection). However, there were 2 or 3 songs specifically arranged (the title music and the password screen).

The complete listing of songs forming the "complete works" for Rockman 3 is as follows:

1) Title Theme
2) Password Screen
3) Stage Select (Rockman Power Battles - Stage Select (Rockman 3~6) - I don't think it was used in the game though)
4) Gemini Man Stage (Rockman Power Fighters)
5) Shadow Man Stage (Rockman Power Fighters)
6) Boss Battle (I think listed as "Continue" on one of the fighter scores)
7) Got Weapon (Rockman Power Fighters - Got Weapon [not used in game])
8) Wily Machine (Rockman Power Fighters)

As an interesting side note, in the anniversary collection, Top Man Stage was replaced with "Mad Grinder Battle" from Power Fighters, which was an arrangement of the Mega Man 7 Intro Stage, but was not Top Man's music.

As for filling out your collection, add any tracks you can get from those arrangements. Also, look for songs by SSNTails (google it) - you can probably get another arrangement or two. Lastly, someone on this forum named Zachary Costa (real name; I don't remember his screen name) did some arrangements for the first 3 games. I have them in a folder that I un-rar-ed that he uploaded called "RRV1," though I don't know if that will help you locate any of it. The quality isn't the same as the Capcom ones, but it's not bad.

Search in Download Links and you should find a Rockman music thread that will have most/all of the music mentioned above.