I have a MySQL database that peaks at about 300 connections/sec.
What is the recommended connections per server and at what point should I start using connection pooling?
IHMO, using of connection pool hasn't a minimum. You can use it when you are sure there are a lot of accesses on your DB and they are very frequently, so you're using the CP guaranteed to use in better way the available connections that caught by users when they are idles.
The numbers of connections must consider the dimension of DB server. There's no a default number that's OK for all configurations.