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.
For Neural Networks there are multiple packages that might help. What have you tried? What didn't work? Here's an article that might be interesting: https://www.kdnuggets.com/2016/08/begineers-guide-neural-networks-r.html
After you do your homework and have some specific questions, come back and I'm bet we can give you more support.