One of the best ways to guarantee perfect circles is to cut them with a die-cut machine (like a Cricut) but assuming that you're not going to become a full time paper crafter $200 might be too much to spend at the moment
You could try folding paper in half, drawing a half circle with a compass, and cutting it out? I was looking at the banner though and was thinking, maybe you can find cute patterned paper plates (where the center is white) and place stickers to spell out what you want? Then there is no cutting/gluing and you will have a perfect circle!
I use ModPodge and a paint brush to glue most of my paper crafts.
Hope this helps!