דבר dbr in the piel is the most commonly used word for "speak":
Am 3:1, 8
the qal has much the same sense: Am 5:10.
dabar "word, message, story or business/affair". The usage in Am 1:1 is discussed in the commentary.
In the prophets the dabar is often the prophet's oracle 3:1; 4:1; 5:1; 7:10 (cf. 7:16; 8:11, 12).
In Amos 3:7 "thing" seems best to describe what God is doing and announcing.
The phrase לֹא דָבָר lo' dabar in Am 6:13 can either mean "nothing" ('no thing') or refer to a town east Jordan (2 Sam 9:4-5; 17:27).
At 1:1, I would like to render dibre as "story" however, I have preferred to avoid an unusual translation in the first verse. (Andersen & Freedman, 184-185 also argue for this meaning, though their translation also reflects the traditional ones, Rudolph used the rendering "story" for the similar phrase in Jeremiah).