Depends on the length.. If the varchar will be 20 characters, and the int is 4, then if you use an int, your index will have FIVE times as many nodes per page of index space on disk... That means that traversing the index will require one fifth as many physical and/or logical reads..
So, if performance is an issue, given the opportunity, always use an integral non-meaningful key (called a surrogate) for your tables, and for Foreign Keys that reference the rows in these tables...
At the same time, to guarantee data consistency, every table where it matters should also have a meaningful non-numeric alternate key, (or unique Index) to ensure that duplicate rows cannot be inserted (duplicate based on meaningful table attributes) .
For the specific use you are talking about (like state lookups ) it really doesn't matter because the size of the table is so small.. In general there is no impact on performance from indices on tables with less than a few thousand rows...