The word "first" transliterated as "barisonah" meaning "at first." Brown-Driver-Briggs lists the meaning under 3.a for Zech 12:7 as "at first, first of all". The NASB concordance includes the meaning of beginning, which is the sense here in Zech. 12:7; so beginning from Judah.
Salvation = the everlasting kingdom of Christ under the new covenant gospel of Christ came first to Judah, and then spread out to all the nations grafted in under the gospel of Christ. This was prophesied from old.
Zech. chap. 12 is a prophesy of the time in which Christ was manifested on earth, when He walked upon the earth of Yehuda / Judah or Judea, in the first century A.D. We have to look at a few key scriptures to determine the time elements and definitions.
The Elements of Zech chap. 12: (Unless otherwise noted, all references are from the KJV)
The people affected = Israel, or the remnant of Israel -
Zech 12:1 "The burden of the word of the Lord for Israel..." is the beginning of a new prophesy, and the people to whom the prophet was speaking
The Time = after the crucifixion of Christ - Zech 12:10,
" And I will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn."
The Branch of David = Christ
" And there shall come forth a rod out of the stem of Jesse, and a Branch shall grow out of his roots: 2 And the spirit of the LORD shall rest upon him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and of the fear of the LORD;"
"5 Behold, the days come, saith the LORD, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth. 6 In his days Judah shall be saved, and Israel shall dwell safely: and this is his name whereby he shall be called, THE LORD OUR RIGHTEOUSNESS."
"14 Behold, the days come, saith the LORD, that I will perform that good thing which I have promised unto the house of Israel and to the house of Judah. 15 In those days, and at that time, will I cause the Branch of righteousness to grow up unto David; and he shall execute judgment and righteousness in the land. 16 In those days shall Judah be saved, and Jerusalem shall dwell safely: and this is the name wherewith she shall be called, The LORD our righteousness."
The house of David = the lineage of the promised Seed, Christ- 1 Chron. 17:23-24,
"23 Therefore now, LORD, let the thing that thou hast spoken concerning thy servant and concerning his house be established for ever, and do as thou hast said. 24 Let it even be established, that thy name may be magnified for ever, saying, The LORD of hosts is the God of Israel, even a God to Israel: and let the house of David thy servant be established before thee."
"5 For there are set thrones of judgment, the thrones of the house of David."
The house of David was also interchangeable with the house of God, as Christ the author of our salvation (Heb. 5:9) reigns on the throne of David:
" The LORD hath sworn in truth unto David; he will not turn from it; Of the fruit of thy body will I set upon thy throne." See also Isa. 9:7;
The elements of this prophesy indicate a time period under the new covenant. so we need to identify the changes in the names and terms from the old covenant to the new covenant.
Jerusalem was the city of David located in Yehuda / Judea under the old covenant. (2 Sam. 5:7; 2 Kings 9:28; 14:20, etc.)
Jerusalem of the new covenant, New Jerusalem, is the bride of Christ, the body and church of Christ. Rev. 3:12,
"12 Him that overcometh will I make a pillar in the temple of my God, and he shall go no more out: and I will write upon him the name of my God, and the name of the city of my God, which is new Jerusalem, which cometh down out of heaven from my God: and I will write upon him my new name."
and Rev. 21:2,
"2 And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband." (See also Gal. 4:26)
Israel under the old covenant was all of the circumcised under the commandment to Abraham (Gen. 17:10) and under the law of Moses (Ex. 12:44, 48).
Israel under the new covenant are all those that are in Christ, and are counted for the seed of Abraham seed (Rom 4:11; 9:8; 1 Cor. 7:18) Because of the two - old covenant Israel and new covenant Israel - He has made both one in Christ Jesus. (Col. 2:6-11; Gal. 4:28)
Therefore, the Israel prophesied to be saved in the Lord with an everlasting salvation (Isa. 45:17), is the Israel of the new covenant under the gospel of Christ joined with all the worthy that had been counted as righteous under the old covenant.
We also note the blessing Jacob gave Judah for their latter days, from Gen 49:10,
"The sceptre shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be."
Christ (Shiloh) received the scepter from Judah, the law giver, when He was crucified on the cross and ascended to the Father in 30 or 31 A.D.
So, salvation - the Messiah - came to Judah first in their latter days, and the gospel of Christ went forward from Judah then to the lost sheep of the house of Israel, and then on to the other nations (gentiles).
See more evidences from the scriptures for the changes in the definitions of Israel and the House of God (God's Definitions, Parts I & II) at my blog: ShreddingTheVeil (All bold emphasis is mine.)