Posting on arxiv is generally considered a good idea if you are worried about competition from similar results. On the other hand, you will give other mathematicians the means to adapt your ideas and possibly prove better, and possibly more abstract results. But hey that's par for the course, and you cannot (or should not want to) hold onto your results forever.

As to where should you submit, I don't think MO users can really tell from the info included in your question. Of course, you should look at journals that have published similar stuff, but isn't this where your supervisor should really come in?

[Added Later: It's not unusual to work with a supervisor who is not a specialist on your topic. It's can be valuable, since it forces you to learn autonomy in research a lot earlier. But whatever your supervisor specialty is, they should be able to give you good advice on the non-technical aspects of your endeavor, including how to write, submit, career advice and so on.]