Sydney airport is unfortunately one of the worst airports in the world for International -> Domestic transfers (and it's even worse in the other direction!).
Terminal 1 (International), and terminals 2/3 (Domestic) are not connected in any way, and are several kilometres apart.
The good news is that recent changes to immigration in Australia - in particular allowing passengers from many countries to use the "Smartgate" automated immigration machines. Even if you're not from one of those countries, the time to get through immigration has been reduced due to them having to manually process fewer people.
The bad news is that once you go through immigration, you need to collect your bags, go through customs (which can also have a delay), and then, somehow, get to the domestic terminal.
If your domestic flight is on either Qantas (NOT including Jetstar flights, even if sold with a Qantas flight number) or Virgin Australia then this is a relatively simply process. Both of these airlines have check-in counters for domestic flights at the international terminal, and both run free buses to the domestic terminal. In both cases, you can use these services regardless of what airline you arrived on - it's just your outgoing flight that matters.
Qantas is a little faster here as you pass through security in the international terminal, the bus runs through the airport, and you arrive airside in the Qantas terminal, whereas the Virgin bus runs landside and thus can be delayed by traffic, and you arrive landside and have to pass through security in the domestic terminal.
Both of these transfer areas are also very good at handing delayed passengers, and will frequently move you to a later flight at no charge if you've missed (or are likely to miss) your original flight - even if they are not responsible for the delay.
If you are flying another airline (eg, Jetstar, Tiger), then you will need to get yourself and your bags to the dometsic terminal, either via public bus, public train, or a taxi. It's not fun, and I don't recommend it.
Time-wise, presuming the outbound flight is with Qantas or Virgin then 2h15 should be fine, but if it was me I would probably recommend going with the 2h45 option just to be safe.
If you are looking at flying with another airline, I would not at all recommend the 2h15 option, and even the 2h45 could be tight depending on things like exactly what time of day you arrive, and how busy the check-in area at the domestic terminal is at the time. Jetstar and Tiger also have very strict check-in/bag drop times, and if you miss it then you've lost your ticket!
It's also a good idea when travelling with multiple tickets like this to have travel insurance. As long as you've over the minimum connection time for the airport (which you are), then travel insurance will normally cover any costs with re-routing if you are delayed and miss the connecting flight.
