I have booked flights to the US on the 29th of June but my J1 visa does not begin until the 19/08. Do I just apply for an ESTA Visa to cover for the time before the exchange period?
Assuming the 19th August is the start date of your program, you can't enter the US in J-1 status until 30 days before the program starts.
To enter in June, you will indeed need an ESTA, but bear in mind that if you enter under the Visa Waiver Program (i.e. with an ESTA), you'll need to exit the US and re-enter using the J-1 before you can begin your program.
You might theoretically be able to avoid this and change status within the US, but that will almost certainly be more hassle than heading to Canada for a day or two.
This thread on Lonely Planet forums has some more info.