If you want to transport a substantial amount of heavy stuff cheaply and time is not important, the obvious solution is transport by sea. There are three options that are worth investigating - which one is best/cheapest (or available at all) will depend completely on your specific origin and destination.
- The postal service may offer sea mail, and books may even get a discount. For example, when I moved from Japan back to Germany, I had about 50kg of books. The Japanese postal service had a special "book bag" rate (you actually got a large canvas bag, and it was restricted to books, with a maximum weight of 30kg).
- Freight companies often take private customers - especially those that compete with the postal service anyway, like DHL and UPS. Smaller ones may be quite cheap (subject to negotiation) but not do door-to-door delivery (i.e. they'll expect you to bring and take the cargo to/from their local office) and take longer while they wait for enough cargo to accumulate to fill a container.
- International moving companies obviously do this kind of thing and are probably your safest bet - just not necessarily the cheapest option. They'll also help you with things like customs.
Customs is something you'll almost certainly have to deal with for this amount of cargo - either by paying it, or by providing documents that prove it's not a commercial shipment.
As for the delivery time to expect - US East coast to Australia would be a minimum of two weeks, but could easily be a month or more if your shipment has to wait for a container to fill up.