A quick summary of what the calvinists and arminians share –

The Gospel of Christ

Christianity as a whole points out the problem in Man and provides the solution in Jesus Christ.
The problem with us is that we are found to be sinful ie evil in the sight of God – and evil is to be rightly destroyed by a good and just God.
And the solution for us from being destroyed under God’s wrath and instead being saved unto eternal life is in Christ providing us the means to be set right/reconciled with the Father – particularly through His death and bodily resurrection.

This offer of salvation is entirely free and wholly initiated by the compassion, kindness and love of God. Man did not merit it in any way and God was in no way obligated to do so and hence we declare this offer of salvation is purely by the grace of God.
And all who put their faith in Christ are promised by God Himself to be saved from death to life.

Both calvinists and arminians believe the above – and in that there is more than enough common ground for both camps to fellowship as brothers and sisters in unity. But then as we take in more of Scripture, division arises.

Election and Predestination

Even so then at this present time also there is a remnant according to the election of grace.

Rom 11:5, KJV

But we speak the wisdom of God in a mystery, even the hidden wisdom, which God ordained before the world unto our glory:

1Cor 2:7

There are clear passages in Scripture which denote that –
1. God did perform an act of choosing or selecting
2. and this was done before the foundations of the world
3. and this was predestined ie there was a specific purpose or end for the fulfillment of which this choosing / (s)electing was done

Both the calvinists and the arminians agree on these too – and this shows that both camps are willing to take in the whole of Scriptures. Where they diverge is in the particular implications – whom did God choose and for what purpose and what other factors played a role in His (s)election?