Using the inet_aton is the right way of doing this, so you're not storing extra meaningless info (no point in being able to store a value greater than 256 for any given 3 numbers). It results in a 32 bit number, which will fit into the unsigned int.
Indexing on the int column will make lookups by IP address quick. If your database gets REALLY big, you'll start running into scaling problems storing this sort of thing in MySQL.
I'll assume you're not going to do that, but will point out that storing complete log info for a large busy site in an RDBMS is generally agreed to be a Bad Thing(tm). You don't need the relational integrity properties the database guarantees, and you write many more entries than you read. Consider nosql, or appending to flat files instead, and parsing your logs when necessary using a dedicated program.