Convolutional Neural Network for Insects
The training set needs to have the same distribution of images as whatever you will be applying your classifier to.  So, if you'll be running the classifier on some images of houseflies and some images of other insects (not house-flies), your training set needs to contain both kinds of images.  If there are many other kinds of non-housefly images you'll be running the classifier on, the training set should contain images of those same kinds of insects, in a similar frequency to the frequency they'll occur when you use the classifier.

I encourage you to read about object classification vs object recognition vs object detection.  See, e.g., https://stackoverflow.com/q/31750076/781723.  The simplest kind of classifier takes an image of a single insect and outputs "housefly" or "not housefly".  That kind of classifier will be trained on images of single insects -- and should only be expected to work correctly if you apply it to images of a single insect.  However, you can also find techniques in the computer vision literature for recognizing the location of the insect in the image and dealing with multiple insects; read about object recognition and detection.

I'm not sure where you got the idea that the default is 2 convolutional layers followed by 2 fully connected layers, but there is no such default and no such rule.  I'm not saying that's an unreasonable starting point, but there are no hard-and-fast rules that tell you how many layers to pick.  Instead, you'll probably need to try several different possibilities and see how well they work.  If you can find papers in the research literature that solve a similar problem, you can sometimes use them as guidance for a good network architecture, but if you're not aware of anything like that, you'll just have to experiment on your own.