Which term and which counter to use when ordering simple meals?
When you don't know the measure word, the safest choice is 个. It is the most common measure word, is used for things that do not have specific measure words, and can sometimes be used even if another measure word is used:

“个”作为一个量词，它的使用范围十分广泛。它可以修饰没有专用量词的名词，如人、馒头、国家、苹果等等；同时，一些有专用量词的事物，如“一只耳朵”、“一所学校”、“一家工厂”等也都可以用“个”来修饰，成为“一个耳朵”、“一个学校”、“一个工厂”，因此，有人称“个”为“万能量词”。
http://www.pep.com.cn/xgjy/hyjx/hyxxzy/hyxx/yffd/201009/t20100901_855523.htm

For food servings, 份 can be used too, but note that it is most properly used on items that are served from a larger whole. For example, this includes rice as it is cooked in one large pot and served in multiple bowls.
Where you can though, try to use the most specific measure word, as it will sound more natural:

Use 碗 for things that are served in bowls, often (plain) rice or soup noodles
Use 盘 for things served in dishes
Use 道 as a generic measure word for food dishes