I'm completely new to ML and what real world applications it's suitable for. Are we at the point yet where you can train a computer to look at arbitrary images and count the number of people in it? What if it was the largely on the same background and only the number of people were changing -- for example, a camera shooting a queue of people to determine queue depth at a bus station.
Convolutional neural nets are the state of the art for this, specifically deep residual learning (http://arxiv.org/abs/1512.03385). It requires a good deal of background to understand what's going on and tune/implement the models, though, even if you just use the frameworks already out there. You probably don't even need that much data - you can probably grab pre-trained models and train them on a small additional dataset you collect.
They can definitely handle arbitrary backgrounds, although having a standard background makes the problem even easier, again.
Most deep learning computer vision algos are trained on 256x256 images, so having even larger images is just fine (you can downsample, or maybe even add up the predictions of different crops).