Autoshrink is usually not a good thing. Shrinking a database in general is not a good thing. In my opinion the only time a database should be shrunk is when the space is desperately needed. By turning autoshrink on you will be hurting performance. It will take processing power to shrink the database, then when more data is inserted it will take processing power to enlarge the database again. Personally I would never use autoshrink and I cant think of any reason to use it.
The performance will become worse. How much worse, depends on how many times you end up expanding the database, and freeing up space. Mostly, this will happen in the transaction log. The short of it is, writing to disk (and expanding/shrinking a file counts as a write to disk) is one of the longest operations in SQL Server.
Suppose you have a batch process that uses up 500 MB of disk space in the transaction log. Suppose also that you have set the recovery to simple. Every night, the database will have to grow the transaction log back up to 500MB, if the database shrinks at any time during the day. THis will prolong the nightly batch job by however long it takes to format the space needed up to 500MB.