FULL DISCLOSURE: I am very anti-Calvinist. But I'll do my level best to give a fair summary.
But if Total Depravity is what you want, then good news! You can believe in Total Depravity without being a Calvinist. That's the one thing Calvinists and Arminians agree on. (And there are other options besides Calvinism and Arminianism, those just happen to butt heads most often. But I'm here on behalf of Arminians.)
Total Depravity doesn't mean that humans are as bad as we can possibly be. It means, more or less, that we can't do anything good without the help of God. Most Arminians would say that even people who don't believe in God can do good things, through Common Grace.
So Arminians agree on that. We generally punt on Perseverance of the Saints. I think most would say that you can deliberately CHOOSE to walk away from God, and God will honor that decision, but that's the only way you can lose it. The only thing that can separate you from the love of God... is you. This is not official consensus however. Calvinists strongly believe in Perseverance of the Saints. If you are truly saved, NOTHING can change that, EVER. If you do fall away from God, that means you were never truly saved in the first place. I find this to be almost a reversal of cause and effect.
Now let's get to the meaty bits, where Calvinists and Arminians hate each other more than Kiwi Farmers and trannies.
Unconditional Election - According to Calvinists, people are chosen for salvation by God, through no merit of their own, solely by God's sovereignty. If people could make the choice themselves, that would (somehow, apparently) diminish God's sovereignty. How does God choose? Well, ALLEGEDLY, God foreknows how a person would have responded to the offer of salvation, and saves or damns them based on that knowledge. Arminians consider this to be crap, and believe that humans make their own choice here. If God is going to be just, he has to treat us according to what we've actually DONE, not what we WOULD do. Free will is a gift from God, and in his sovereignty he allows us this important choice. We couldn't make it on our own, without his help, but when God makes the offer we can freely choose to accept or reject it.
Irresistible Grace - Calvinists believe that when God offers salvation to someone, that offer will ALWAYS been accepted. For us to refuse it would be to diminish God's sovereignty, and would question if God really did foreknow who would accept or reject him. Arminians also consider this crap, basically for the same reason as the last one. We have a choice, because that choice is given to us by God.
Limited Atonement - Calvinists believe that Jesus died and atoned only for the saved. Arminians believe Jesus died for everyone, even those who reject him. Of course, as above, anyone can still refuse that gift. (I would go further and say that Jesus died for the entire universe, not just humans, but that's another topic.)
Here's the problem. Calvinism sacrifices God's justice and love for the sake of his (perceived) sovereignty. Calvinists believe that giving humans that level of freedom elevates us too much, and diminishes God. But an Arminian would say that if we have that choice because that's how God wanted things to be, then that doesn't diminish God's glory at all. On the contrary, he's even greater that he would make beings with such freedom. It's also the only way to defend God's justice, because Calvin's God is a tyrant who arbitrarily selects humans for salvation or damnation.
PS - Most of what I know about Calvinism came from a book by a Calvinist, called Willing to Believe. It made me not be a Calvinist.