Neon tetras and goldfish require different water temperatures. The neons are actually quite sensitive, (contrary to popular belief) and will soon become lethargic and prone to lots of illnesses if kept in cool waters. So there goes your worry of them eating each other's foods. Another thing I'd be worried about with tetras in a goldfish tank is that, as goldfish are opportunistic feeders, they might eat the smaller neon tetras (who could quite easily fit into the mouths of adult goldfish).
Bearing this in mind, while a goldfish is still juvenile it can be kept with White Cloud Mountain Minnows (WCMM), which prefer cooler waters and shouldn't be eaten if the goldfish is young.
However, goldfish are sociable fish so would prefer to be with other goldfish. In a tank that large you can put another goldfish (providing they are both fancy), and that would be fine. If they were common/comet goldfish then they would need 55 gallons, so 100-110 for 2. Make sure your filtration is double the size of the tank itself! So I hope your filtration is for 150 gallons :)