Your splice is one obvious inefficiency. You could push onto another array or grep. The resulting array of indexes could be used in a slice of @Persons.
Where is @Persons populated from? If a file, you could do your filtering as you read it. If a database, you can make it do all the work.
To make executable filters from form data, be cautious. You'll be tempted to eval, but that is inviting trouble. Try setting up a dispatch table (a hash of code references) of functions to call via the field names, with field name and value as arguments. Where you have several fields, grep is again your friend.