Short version: yes you should wait until september to use throwback tickets but i'm unsure even with a month of rewards if you can keep up with throwback.

Long version: Yeah you can use throwback rotation pack tickets in september and the cards will last you a month. But when it rotates its 5 different card sets not just one added on like old rotation, so you're trying to keep up with resources on many more sets than before throwback rotation existed, and personally i can't say how easy it is to keep up with that because i joined earlier. Also trial decks existed in old rotation so you could get one free deck per expansion and swap out a few cards to have a meta deck in some cases, but that doesn't exist for throwback. When i started the game with normal rotation putting no money in, i had 1-2 decks for the first half a year or slightly more and i only had to keep up with them adding one expansion at a time. The other modes like unlimited or custom rotation are safer for new players bcuz you can keep using same deck, but less balanced so they can be less fun and custom rotation only has unranked so you're missing some rewards by playing it.

If you do the elite AI battles in practice mode you'll get rupies from the achievements tab and story mode also gives rupies, its a good amount for new players but you can only get those rewards once.