John Frame's Systematic Theology, chapter 13
God is the "perfect internal standard of right and wrong." The moral law is based on His being; not above Him or changeable by Him, but an expression of Him. So we are to be holy because He is (Lev. 19:2). We imitate Christ (Eph 4:22-24; Col 3:10).
Righteousness is a forensic word, with a context of law and courtroom. There are penalties for breaking God's law.
The Bible also speaks of His righteousness as actively bringing salvation to people. Psalm 9:7-9; Isa. 46:12-13. He is faithful and just to forgive us (1 John 1:9). He vindicates the righteous against His enemies (Ps 34:15-22; 72:1-4). This isn't traditional Liberation Theology, where God always delivers or is on the side of the economically poor. He gives justice to His people (Luke 18:7).
By the sacrifice of the Righteous One, we become the righteousness of God (2 Cor 5:21).
Zeal to guard exclusiveness of a relationship. Scripture always speaks positively of jealousy, and Ex 20:5 is clear that God is jealous. His zeal is for His name to be hallowed and honored. Jealousy is an expression of love, not its opposite. If you shrug at your spouse's infidelity you do not love him/her.
We should love people instead of hate them, but God calls us to hate evil.
God directs hate at sinners sometimes, not just their sin (Psalm 139:21-22; 119:113).
Hatred doesn't always involve hostility, disgust, or seeking the worst for someone. It can be merely relative priorities (Gen 29:31; Matt 10:37), or opposing one's plans or intentions. In this sense you can both love and hate the same person. This is important, or we could not say "God is love" and also affirm that God hates at all. But "God is the supreme hater of wickedness."
We should pray imprecatory Psalms against God's enemies, calling God to judge them, while also desiring their conversion. Those God hates at one point in time may be converted later on - we were all under His wrath once (Eph 2:3) but He saved us. God hated Esau from his birth (Rom 9:11), but this regards historical election. Paul is using that to explain eternal election, but Esau himself was not necessarily eternal damned.
Though Scripture often warns us against being angry as a sin (Matt 5:21; Gal 5:20), there is also a righteous anger Jesus displayed (John 2:14-17) and that God has in response to sin (Jer 6:11). The Bible often refers to wrath with no connection to God (Num 1:53; Rom 2:8), but it's implied. Even the Lamb executes His wrath (Rev 6:16-17), God threatens wrath against Moses (Ex 4:24) and Israel at Sinai (Ex 19:24). HE is a a consuming fire, and it's fearful to fall into His hands. We tend to diminish the intensity and frequency of references to this in Scripture. This may be okay, as Scripture itself does so with brief descriptions of "wrath."
God is slow to anger (Ps 103:8) and flows righteously from His jealousy. It is "but for a moment" for His people (Ps 30:4-5), but enduring for the unrepentant (Matt:8:12; 25:30).
God is different from us. Moses stood on holy ground at the burning bush because God was there. The temple and tabernacle show varying degrees of holy places, not a holy/common dichotomy or a sacred/secular distinction. Holiness means God's otherness brings us to wonder, awe and fear of Him. It also reminds us we are undone before Him as sinners. Both God and sinners draw back from each other because of the ethical difference. (Think of Peter telling Jesus to "Depart from me.") But God also draws us to Himself, making us holy and calling us to be holy as He is. He gives Israel a festal and temple system to enter His holiness, as He gives us Christ to do the same more fully. Frame says God's holiness moves Him to mercy, appealing to Hosea 11:9 and Ps 22:1-5. It seems to me that other attributes of God move Him to draw us to Himself more.