the who goes where and roughly how much question is something http://www.skyscanner.net is useful for. But which August? If you mean this year then by now prices will be very fluid and changing daily and could even book up whilst you think about it. If you mean next year not all operators will have released seats so the comparison won't work. Also the comparison won't include the various extra charges that crop up - like baggage, check in and booking fees.

Using TR is not technically DIY (I'm being a pedant). But now you've mentioned them, we have found that the dreaded extra charges on flights may be less if booked through them with the accomodation, Ryanair was an example where money could be saved.

You could try using TR to find suitable accomodation and then look it up on the web and see it is cheaper booked direct, although that may not mean easier.

If you do book DIY or under "not packaged" conditions you need to make sure you have adequate insurance with Supplier Failure Cover. If you spent £1000 on flights and £3000 on accomodation and the outward flight was cancelled, the airline is only liable to refund the £1000, and you have no claim against the accomodation supplier so could lose the £3000. With these sums of money it's probably a good idea to find the insurance before you book anything.