Limited data for low-resource languages typically yields weaker language models (LMs). Since pre-training is compute-intensive, it is more pragmatic to target improvements during fine-tuning. In this work, we examine the use of Active Learning (AL) methods augmented by structured data selection strategies across epochs, which we term 'Active Learning schedulers,' to boost the fine-tuning process with a limited amount of training data. We connect the AL process to data clustering and propose an integrated fine-tuning pipeline that systematically combines AL, data clustering, and dynamic data selection schedulers to enhance models' performance. Several experiments on the Slovak, Maltese, Icelandic, and Turkish languages show that the use of clustering during the fine-tuning phase together with novel AL scheduling can for models simultaneously yield annotation savings up to 30% and performance improvements up to four F1 score points, while also providing better fine-tuning stability.