If you book a cheap ticket via the website which isn't part of your overall itinery then you could have problems if your incoming flight is delayed and you miss your connection. If the connecting flight isn't on the same itinerary then I believe that the airline can just wash their hands of any responsibility even if it is the same one for both the international and domestic legs.
But then if you wait until arriving and take pot luck you could end up either with very expensive tickets or with no tickets at all, depending on the actual circumstances of the day. On the other hand you could end up with bargains. Market conditions will rule!
If you intend to fly your choice depends on your risk profile. If you're risk averse you should book a through ticket, if not take one of the other options.