Who is it that God has given to Christ? Interestingly, the section of scripture you used to try to disprove particular redemption says exactly who God gave Christ.
First of all, the text that you referred to is speaking of that moment when Jesus was made a little lower than the angels. The text goes on to explain that this was for, or by, the suffering of death to the end that He should taste death for every man. Now many latch on to that last part but fail to keep reading. The next few texts read like this: "For it became him, for whom are all things, and by whom are all things, in bringing many sons unto glory, to make the captain of their salvation perfect through sufferings. For both he that sanctifieth and they who are sanctified are all of one: for which cause he is not ashamed to call them brethren, saying, I will declare thy name unto my brethren, in the midst of the church will I sing praise unto thee. And again, I will put my trust in him. And again, Behold I and the children which God hath given me. Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil; and deliver them who through fear of death were all their lifetime subject to bondage. For verily he took not on him the nature of angels; but he took on him the seed of Abraham. Wherefore in all things it behoved him to be made like unto his brethren, that he might be a merciful and faithful high priest in things pertaining to God, to make reconciliation for the sins of the people. For in that he himself hath suffered being tempted, he is able to succour them that are tempted."
Now that was a lot of scripture, but it was important to look at the whole passage, because it is all interconnected. You see the word "for" a lot, meaning that the scripture is explaining itself further, connecting itself together. This section of scripture is really explaining why Jesus took on Himself human nature and suffered on the cross. It was to "taste death for every man." But, then the scripture goes on to explain that He was bringing many sons unto glory, that He is the captain of their (the sons brought unto glory) salvation, and that He was made perfect through suffering (that suffering being that of the cross). Now, the scripture goes on to say that He is not ashamed to call these sons brethren, and even identifies them as the children which God gave Him. Who did God give Christ? He gave Him children, the sons brought unto glory, the every man Christ tasted death for. You see how these texts are talking about what Christ did on the cross and why He did it. He took on Himself the nature of His brethren, that He might destroy death for them and deliver them from the bondage they were held under. It was their sins He made reconciliation for. When Christ tasted death for every man He did so for the cause that they wouldn't, to the end that they would be brought unto glory and freed from death and him that had the power of death. This is why He was made flesh and suffered. The every man He suffered for are the children given Him, to whom He gives eternal life, of whom He will not lose one but raise them up again. He didn't taste death for Judas Iscariot who was and is a devil, who betrayed Him, who it would have been better for him had he not been born. He died for God's people, the ones given Him, to the end that not one would be lost.