PHP can, properly used, can handle as large a website as you wish you build.
MySQL does fine as long as the simo connection rate isn't too high, but currently lacks the advanced locking mechanisms needed for use in larger apps like transactional systems, 0r systems where hundreds of people interact at once.
That said, for the intermediate size intranet type application, mySQL can fly at certain tasks, like message database and such.
If money were no object, you could look at db2, oracle, informix or sybase.
For free, you have a choice between mySQL and postgresql. Postgresl is a full featured, nearly SQL92 compliant database, that has made quantum leaps in performance and bug fixes with version 7.0.2. It's multi-backend design with a large shared buffer makes it scale pretty well on multi-CPU hardware, as long as you have the I/O bandwidth to handle it. Our testing found 6.5.3 to be about 10-20% slower than Oracle or db2, and it feels like 7.0.2 is about even with both of them on single CPU machines.
Note that for development or personal use, db2 personal edition is FREE, and I think oracle has an eval version for linux as well.
We'll be getting a dual 750 PIII to test it on soon, so I'll do some benchmarks with it comparing pgsql 7.0.2, 6.5.3, db2, mysql, and a few others.