Hey George. You're going to struggle a bit getting help with a question this broad. To be honest I'm not even sure what you're really asking, which makes it hard to give you help. You mention "readmission healthcare data" which sounds interesting. Is this public data you can share?

Then you mention three things you would like to use: Trees, Log Reg, Neural Net. For a tree based model, like CART the rpart package does make sense. You seem to know that. So what's your question? Have you tried it? Did you get an error?

For 'log reg' I am assuming you mean Logistic Regression. That comes built into R via the Core R package stats and can be built using the glm function. Datacamp has done an pretty good intro to Logistic Regression that you may find useful: https://www.datacamp.com/community/tutorials/logistic-regression-R If you have some specific questions, please ask.