500k daily it's just 5-7 queries per second. If each request will be served for 0.2 sec, then you will have almost 0 simultaneous queries, so there is nothing to worry about.
Even if you will have 5 times more users - all should work fine.
You can just use INSERT DELAYED and tune your mysql.
About tuning: http://www.day32.com/MySQL/ - there is very useful script (will change nothing, just show you the tips how to optimize settings).
You can use memcache or APC to write log there first, but with using INSERT DELAYED MySQL will do almost same work, and will do it better :)
Do not use files for this. DB will serve locks much better, than PHP. It's not so trivial to write effective mutexes, so let DB (or memcache, APC) do this work.
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