I want to learn to read and write in all the four South Indian languages - Tamil, Telugu, Kannada, and Malayalam. What should the ideal order be if I'm primarily interested in the literature of South India?

If you are a North Indian (or non-South-Indian), I'd suggest you to go with Telugu. Because, Telugu has a fair share of its roots from Sanskrit, and Tamil. Since most of the non-South-Indian languages have a fair share of influence from Sanskrit/Hindi, Telugu will be the way to evolve your native understanding of the vocabulary, phonetics, sentence structuring, into a South-Indian language. You will notice that Tamil has much lesser number of alphabets, so that increases its difficulty in adapting to it (from a non-South-Indian point of view). Learning Tamil after you learn Telugu will give you a great advantage of being in a much better and evolved state of your learning experience. Telugu will be your midway to, a cross-road of, cultures, lifestyle, language, and speech. Kannada and Telugu only have similar scriptures. While Telugu is closer to Sanskrit, Kannada is closer to Tamil, in its style. Malayalam, on the other hand, also has a great influence from Sanskrit in its phonetics, but also has several tongue-twisting and nasal sounds, making it completely alien-like for a non-South-Indian to learn it. Therefore, I'd recommend you to learn the South-Indian languages in either of the following sequences: 1. Telugu - Kannada - Tamil - Malayalam 2. Telugu - Tamil - Kannada - Malayalam

First do learn Tamil. It is quite tough. Telugu and Kannada are very much similar when it comes to writing. So you can choose the order either way. Then you can learn Malayalam which will help you due to your  Tamil experience.

Go on with Tamil first, then it will be easier to learn malayalam. If you have known sanskrit/hindi, as you have already learnt tamil, it will be easier to learn telugu and kannada. Telugu and Kannada share almost same script too.  Both these languages has some Tamil and more sanskrit words.

Tamil will be first in order because its bit tough, if you are good in Tamil then Malayalam. There are lot of common words shared in Tamil and Malayalam so you won't be having difficulties. Then Kannada or Telugu both has same script . Over all if you are fluent in Tamil ,Telugu and Malayalam will be easy to understand .

Telugu is very different from the rest grammatically. Tamil and Kannada are very similar in grammar but not in pronunciation. Kannada and Telugu are very similar in pronunciation but grammatically quite different. Kannada and Telugu scripts are similar. I have heard that Tamil and Malayalam are quite hard to pronounce for non-native speaker compared to Telugu and Kannada. Isuggest, If you live in Bengaluru then learn Kannada first otherwise Telugu.

Start watching other language movies(good ones) with english sub titles. Make friends of these languages and listen to them when they are speaking. Start replying to them in their languages. This will be a good start. Then you can go to the books to read and write.