The availability of different pre-trained semantic models has enabled the quick development of machine learning components for downstream applications. However, even if texts are abundant for low-resource languages, there are very few semantic models publicly available. Most of the publicly available pre-trained models are usually built as a multilingual version of semantic models that will not fit well with the need for low-resource languages. We introduce different semantic models for Amharic, a morphologically complex Ethio-Semitic language. After we investigate the publicly available pre-trained semantic models, we fine-tune two pre-trained models and train seven new different models. The models include Word2Vec embeddings, distributional thesaurus (DT), BERT-like contextual embeddings, and DT embeddings obtained via network embedding algorithms. Moreover, we employ these models for different NLP tasks and study their impact. We find that newly-trained models perform better than pre-trained multilingual models. Furthermore, models based on contextual embeddings from FLAIR and RoBERTa perform better than word2Vec models for the NER and POS tagging tasks. DT-based network embeddings are suitable for the sentiment classification task. We publicly release all the semantic models, machine learning components, and several benchmark datasets such as NER, POS tagging, sentiment classification, as well as Amharic versions of WordSim353 and SimLex999.