If you are happy to commit to specific trains, book Advance single tickets on the Southern Website, but if you miss the specified train your ticket has no value and a new ticket would need to be purchased.
For walk-on travel a Clapham Junction (CLJ) to Brighton (BTN) Anytime Day Return with a Railcard is £16.85. This is valid at any time, to return the same day. There is no 3-day product that I am aware of.
"Splitting" the journey into a combination of tickets is not normally useful for pre-10am travel with a 16-25 Railcard, due to the £12 minimum fare on most walk-on tickets, however this does not apply (ie, there is not a minimum fare) during July/August, so for the dates you mention it may be a possibility. Perhaps someone who is based in that area can advise.
(PS: Any chance of a more descriptive username?)