SQlite foreign key logic

I am using SQlite and the PK column seems to be auto-incrementing. I am a bit concerned about following approach where I want to normalize the type-column:

Table: Book
id   type  name
...  ...   ...
15    1     Foo
16    2     Bar
...   ...  ...


Table: Type
id  typename
1   magazine
2   novel

What happens, if I recreate the Type-table and the PK-index (="id") changes, e.g. that 1 now refers to novel instead of magazine. So to be more robust, I am thinking about inserting a custom second column that contains the "logical" indices that I refer to:

Table: Book
id   type  name
1    3     Foo
2    4     Bar

Table: Type
id   type  typename
1    3     magazine
2    4     novel

This way my custom type-ids would be independent from the primary keys. I think another advantage of the last approach is that I would not have to re-ask the latest (new) id of a new row, because I would refer to the type column that I know before. This way when I insert the row I already know the "type" id to make references (I am using threads for the database, so reading a value from the database within a method is difficult or not possible (?) - so if I would need the id, I would have to ask the db first).

Is this a legit approach? Or should I directly create a non-incrementing primary key with my "custom id's" that I manage on my own?