The cage I have for my Quaker has 1/2'' bar spacing. I think 3/4'' might be pushing it... I would honestly go 5/8'' max, especially if you're going to be bringing home a just weaned baby.
ETA: This is the cage I have for my little guy. I really like it.
Sully-2 year old cinnamon and Bella-3 year old normal
breeding pair of gcc, Scooter & BeeBee-Sully and Bella's normal son's, Rosey- Bella and Sully's cinnamon daughter, Ella & Sunny-American budgies
Whitefaced Pied Male Tiel- official greeter at the Rainbow Bridge, forever in our hearts,
Turquoise Mutation IRN,
Congo African Grey- please come home to us,
Blue mutation IRN
Sprite has 3/4 bar spacing and I don't think he would ever escape through the bars. EVER! lol! And quakers are bigger than Sprite, so I think he'd be just fine in a 3/4 bar spacing.
Sully-2 year old cinnamon and Bella-3 year old normal
breeding pair of gcc, Scooter & BeeBee-Sully and Bella's normal son's, Rosey- Bella and Sully's cinnamon daughter, Ella & Sunny-American budgies