First, a definition
What you are asking for is called a frame story. Imagine your novel as a picture on a wall. The protagonist of your novel and his activities set the frame of the picture, the things that are happening outside. The short story he has written is the picture itself, the thing that happens inside the novel.
Second, do research
Now that you what you're looking for, you can do some basic Google searches for "How to write a frame story" and get a more general answer to your question. Here are some good resources I found while browsing:
- LiteraryDevices lists many good examples you can read for research.
- Sophia.org has a tutorial with visual depictions.
- WriteOnSisters suggests some tips you'll need to keep the story straight.
- And on our very own Writers.SE, Paul A. Clayton wrote this great answer to a related question.
These are by no means the only good resources, simply the first three I found in a basic Internet search. Once you get a general overview of your problem, find some in-depth writing books that discuss it. Look at the great wealth of books on writing that exist. Pick some and read them, taking notes the whole time. This should be done concurrently with my next step...
Third, read like a writer
A key step is finding literary works that display the technique you'd like to use and then reading them while taking notes on how they effectively accomplish it, exactly as Mbakeranalecta suggested. You can get many suggestions here and from the above links.
It's not enough to just read the book. You have to read like a writer. Read it once, to enjoy it and to get a general feel for what happens. Then read it again. Take notes:
- Where is the frame story written? Where is the interior story written?
- How much space does the author develop for each part?
- How often do they switch between the two stories? At what points do they switch - at a climax? After resolutions?
- What literary techniques do they use to mark the difference between the two stories? Do they use different perspectives, as you suggested using? Do they use different tenses (past vs present)?
- What do you love about their work? What do you wish they did differently?
Ask yourself all these questions and more. Ask yourself what you need to know to reproduce this in your own work, and then find that information in the established literature. Read like a writer.
This may seem an obvious step, but many new writers struggle with it. In order to be a writer, you have to actually write. It is essential to finish what you begin. Finishing your works will teach you far more than I ever can convey on this Internet forum.
I will say that I like your idea to have the frame story in one perspective (in this case, first person limited) and the inner story in a different perspective (in this case, third person omniscient). I think this will do a great job of seperating the two stories from each other and, coupled with other literary techniques, should make it fairly easy for audiences to follow the transition. Other, more specific tips, you will have to discover for yourself.