Seen off by my whole family, I shoulder the backpack I'd packed for the trip.
Literal
I [topic-は] family all-members [by-に] seen-off-[while-ながら], travel-preparations [object-を] arranged rucksack [object-を] shoulder.
旅支度 ('travel preparations') is a compound of 旅 'trip' + 支度 'preparations.' ザック is a loanword from German Rucksack, shortened — common among hikers. 見送られながら ('while being seen off') is passive + simultaneous. The present-tense 担ぐ at the end gives immediacy to the departure scene, as if narrating in real time.