Choice of DB is up to you, but MySQL is usually the default on a lot of distros.
If you're already using MySQL (albeit from a 3rd party), I'd stick with that; less confusing.
You have a couple of choices
a) create the new DB instance on a new system
b) add a new schema to the current DB instance. This won't interfere, so long as you create a new user (ie schema owner) etc for it.
Its useful you're using Perl, because Perl has modules for dealing with almost any DB, including MySQL; been there, done that, got the T-Shirt
You could also do the web pages in Perl, although you'll also find a lot of recommendations to use php for that, because a lot of web hosters supply that as std.
Its your choice....