Here's something to start:
A little about me
I am a Christian and a Baptist. I studied theology, graduated from a Baptist university and a Baptist seminary. I am ordained and a licensed preacher (I am licensed by a Baptist church), but I have never pastored a church.
I was a Calvinist for years. I taught Calvinism (when teaching theology), and to be honest I am sure Calvinism influenced by preaching and teaching. I abandoned Calvinism for its’ presuppositions as they were, in my view, too foundational to Calvinistic doctrine to be assumed rather than present in Scripture. Also, I found the assumptions to be inadequately defended when challenged by several scholars.
Calvinistic assumptions
I am assuming by Thomist you are speaking of not only philosophy but also his view of Christ’s work and redemption. If so, you are in a fairly good place to learn about Calvinism.
By training John Calvin was not a theologian, but a lawyer. Calvinism starts off with Calvin’s reworking of Aquinas’ theory of the Cross. The major difference is what the work of Christ accomplished, how this was accomplished, and the effects of sin.
Calvin spiritualized everything into a court-room type arena and defined the “problem of sin” to be one centered in divine justice. Calvin rejected Aquinas’ view of justice, replacing it with a retributive justice that had legal demands.
So the cross becomes the point where men are redeemed by legal requirements being met to satisfy the demands of divine justice. Divine justice being satisfied God is free to forgive the men for whom this debt was paid.
God took man's punishment upon Himself by the Father (God) punishing His Son (God) on the Cross to satisfy the demands of divine justice by paying the debt of sin for individual men. This act on the cross was God's act of forgiving man (the philosophy is that God has to receive payment of a debt in order to forgive the debt, but in actuality the act constitutes forgiveness).
Calvinism
Here - on the Baptist Board - Calvinism is a neo-Calvinistic theology (it is not traditional Calvinism but rather an expression in five points – T.U.L.I.P.). The Canons of Dort are generally accepted however non-Baptist doctrines are passed over and the remainder is held by Calvinists to varying degrees.
Men are totally depraved and there is nothing in man that can turn them towards God. This can only be done by God.
If you begin with the Calvinistic presuppositions then every sin must be paid prior to the sinner being forgiven those sins (or as a means of forgiveness itself).
Therefore Christ had to have died only for those who would be saved, otherwise He would have paid the debt for people who would ultimately still be condemned and God would be unjust.
Election is individual.
God chose who would be saved either from fallen man or prior to the fall of man (this is debatable among Calvinists). God’s choosing was not by chance, but by God’s plan and design which is beyond our knowledge. But God did not choose man on any condition present within that man.