A summary of John Frame's Systematic Theology, chapter 16
God is powerful and no one can resist Him.
Gen 18:14; Luke 1:38; Mark 14:36.
GOd can't do illogical, immoral, changeable or God-denying things. These don't imply lack of power. Some inability is admirable.
Omnipotence is hard to define. He can do what Scripture describes Him doing, and more, according to His attributes. ["God can do all things except immoral, illogical, changeable or God-denying things" seems helpful to me.]
Omnipotence edifies - this characteristic of God drives us to worship, as God acts beyond our expectations. Sarah gives birth, and Mary; exodus; resurrection.
Omnipotence is often found in weakness (2 Cor 12:9). Power of God shown in the cross (1 Cor 1:23-25) and in preaching (Rom 1:16).
The will of God is what He decides, what He wants to happen.
God's antecedent will (He generally values things as good) is distinguished from His consequent will (He chooses to enact some of those things). This can't place God's choices within time, though, nor make His consequent will to save us dependent on our choice to repent and believe.
God's decretive will (He foreordains all that comes to pass) is distinguished from His preceptive will (He values certain morals or states of affairs that men can resist and flout).
So God's will is complex, though not dual or schizophrenic. Scripture speaks of His will both decretally (Matt 11:26; Gen 50:20) and preceptively (Ezek 18:23; 2 Peter 3:9; Ex 20).
Can God really want all to be saved, though it doesn't happen? Yes. Many passages point to this - Deut 5:29; Matt 23:37; 2 Pet 3:9; 1 Tim 2:4.
We shouldn't try to choose God's decrees or precepts as His REAL will.
What about God's will for my life? This gets too subjective, usually, and people usually discern it through emotions or feelings - a bad idea. That doesn't mean we cannot discern the will of God for us in a given situation. We must look to Scripture first, then use wisdom by the Holy Spirit to apply the Word to us. Often more than one option before us is legitimate Scripturally, but weighing the pros and cons may reveal that we can glorify and obey God better in one option than in another.
A third category of God's will, besides decree and precept, may be useful for this, His vocational will (what He's calling us to do), but this is really part of His preceptive will applied to each person.
These categories fit in Frame's standard tri-perspectival triangle (normative at top, situational at bottom left, existential at bottom right).
God's preceptive will is normative.
God's decretal will is situational (He puts us in circumstances to learn certain things)
God's vocational will is existential