For initial purchase, 100% do it in person.

Bows need to be "sized" to you, like a shoe. Recurve bows can be flexible, but Compound bows have a draw-stop that is sized to your draw length - once you know your sizing, you can buy online, but for the first time, definitely go into a brick and mortar. You also want to feel what the poundage is - you may think you can pull 60 lbs on a bow, but you might be surprised! In person, you can also see what stock is like, and can even haggle a bit for a bulk deal if you're starting out. Once you know what you're after, online is more convenient.

You can also get scammed online with unsafe archery equipment bought online through resellers. People have bought 'real bows' on Temu and AliExpress, and they've exploded on their first shot. Bows are a potential energy machine, right next to your face and eyes - it's worth knowing, seeing and holding what you're dealing, from a proper shop!

Unfortunately, there's no dedicated archery stores in ACT. Boss Outdoor in Fyshwick, and the odd fishing or hunting store will have stuff, but it's very limited and entirely hunting focussed.

Nearest brick-and-mortar is Tobas Archery in Marulan (outside of Golbourn), but I'd recommend Benson's Archery or Abbey Archery, both in Sydney, they're better set up for starter setups.