Your athlete will want good supportive running shoes but they do not have to be expensive.
Separate from running shoes, track spikes are not required but helpful. We are building a team collection of used spikes that increases as athletes grow out of their spikes and donate. ebay is a great resource for finding lightly used or new spikes, often at half the cost of store bought spikes. $25-$35 is a great range. At youth age levels, the improvement in expensive spikes is negligeble compared to the other ways an athlete can improve.
Sprinters, distance runners, throwers, and jumpers all have different shoes at the higher competitive levels. But as youth, follow these simple guidelines. Sprinters and jumpers: track spikes should be light with no heel cushion. Distance: thicker heel cushion. Throwers: no spikes with flat smooth tread. If your athlete does multiple or all: get distance spikes and wear running shoes for throwing.