The answer depends on a number of factors:
How much load are you expecting? If this is an intranet solution to be used by 4 or 5 people on an infrequent basis, the built in SQLLite may be sufficient. If this is a public facing web application which is expected to receive hundreds of orders every day, you'll probably want to run a MySQL or PostgreSQL server alongside it on the same server. If you're looking at hundreds of thousands of orders, you'll most likely want MySQL or PostgreSQL running on a separate server.
If you've got coders with development expertise on Oracle, Sybase, etc.. it might be worthwhile investing in those. If you've got all coders who are just starting out, or who have experience with MySQL, or PostgreSQL, then obviously that makes more sense.
Also consider if there are any other systems which the application interfaces with. If you're going to be working with an order fulfillment system which requires Oracle, then you'll probably want Oracle.