Unless you're using unsupervised learning or can find a good dataset, most of the cost will be in labeling the data. I'm not too familiar with background removal, there may be some self-supervised/contrastive learning approaches, but generally they don't work as well as supervised learning. Even for a week of training, the compute cost is only $200.

Edit: maybe you can get some decent results just with COCO segmentation labels: https://towardsdatascience.com/background-removal-with-deep-...