We believe in the Holy Trinity consisting of God the Father, Jesus Christ, His only begotten Son, and the Holy Spirit. We believe this triune God to be perfect in every way and worthy of our complete devotion and worship. We believe that all mankind is born into sin, separated from God and destined to an eternal destiny apart from God. We believe that God, in his infinite love, has provided a way for us to attain relationship with Him, by sending His son to be born as a man, to suffer, and to die in our place. We believe that on the third day after His death, Jesus Christ was resurrected and now sits at the right hand of God, interceding for us. We believe that we are saved by faith in Jesus Christ and that faith will be manifested thru obedience to Christ. We believe the bible to be the infallible Word of God and the final authority on all matters. We believe that God has called us to live holy lives, as He did, and desires us to honor Him by caring for the poor and needy and by setting free those who are held captive by the devil. We believe that when life on earth is over, those who have repented of their sins, accepted Jesus Christ as their savior, and have strived to walk as He did, will be united with Him forever in heaven.
The disagreement between Calvinists and Arminians are over the precise nature of predestination and election. The traditional Arminian position can be seen in the Five Articles of Remonstrance. The key difference between an Arminian and Calvinist position is that of free will: Arminians believe that human beings are born with free will, and can therefore resist God's grace. Salvation is, from this perspective, conditional on whether a man or woman accepts God's grace.
By contrast, the traditional Calvinist / Reformed view is that mankind does not have free will, we are incapable of accepting salvation unless God himself enables us.
This is how the 39 Articles of the Church of England puts it:
X. Of Free-Will
The condition of Man after the fall of Adam is such, that he cannot turn and prepare himself, by his own natural strength and good works, to faith; and calling upon God. Wherefore we have no power to do good works pleasant and acceptable to God, without the grace of God by Christ preventing us, that we may have a good will, and working with us, when we have that good will. Source
The statement of faith you cite does not actually take a position on these things. I would suggest this is almost certainly intentional. Some denominations or churches do not want to take a position on this, for fear that they will alienate some people. Many churches simply want to focus on what unites, rather than what some say are more contentious issues.
There are no doubt arguments to be had of the wisdom of such an approach, but perhaps to go into it would be beyond the scope of this answer!