the needed spine depends on multiple factors.. As Mark mentioned, arrow length is a factor along with point weight. Store bought arrows for lighter weight bows are generally inexpensive (child) arrrows, or very expensive womens recurve target arrows. If you pick up a few of the inexpensive ones at the department store, you might try replacing the plastic vanes with softer feathers. I use hotmelt glue to add various tips for additional weight.
A self bow with a wider arrowpass generally requires more arrow tuning than a centershot bow, so I prefer to rip clear spf on the table saw and shape with a $10 thumbplane, rather than be buying lots of parts and pieces for a carbon or aluminum arrow. Others prefer shoots or bamboo/cane