Algorithm suggestion for ticket routing system using Machine Learning Background info

I'm a beginner in ML, let me start there. I'm trying to implement an intelligent system that can route a ticket (in a ticketing system), to the appropriate place based on a few parameters, 5-10.

How the algorithm should work

For example, ticket '1234' gets sent to 'accounting' by human, normally by reading the ticket description and title (finding keywords). The ML algorithm should learn where tickets go based on where similar (based on same keywords) tickets have gone before.

What I've tried

I implemented a very simple NN in JavaScript using the sigmoid function to predict discrete yes/no type of outputs. If I remove the sigmoid function, I could predict where the ticket should go, based on keywords turned into parameters, perhaps using linear regression.

The problem

I'm not sure how I can turn keywords into number parameters, (or vectors?), that can be fed into a simple linear regression implementation. With my limited knowledge, I'm not sure if linear regression is the way to go but it certainly sounds like it. Linear regression is also a simpler algorithm I'll be able to implement myself.

Is linear regression the way to go? How can I turn an arbitrary-length paragraph (ticket description) into meaningful keywords to be used by the algorithm?

Ideally this would be JavaScript, but I see no tags for JavaScript. Odd.
Linear regression does not seem like the right tool here.  This isn't a regression problem; it is a classification problem.  Regression outputs a continuous number; you need to output a category (which place the ticket should be routed to; presumably there is a finite list of candidate places).

I would suggest that you learn about natural language processing.  The very simplest thing you could try would be naive Bayes with bag-of-words features.  Fair warning: I would not expect that you will get especially good results without a lot of knowledge of NLP (and maybe not even then); it's probably going to be challenging to find a good solution for your problem.