Automated brain tumor classification is an intensively investigated problem, which recently attracted significant attention. Convolutional neural networks (CNN) and deep learning represent the standard for the foundation of any recent solution. This paper proposes two simplified VGG architectures and investigates their capabilities and limitations, in comparison with state-of-the-art CNN networks deployed via transfer learning. Various parameter settings are involved in the evaluation process, including different kernel sizes, dropout rules, loss functions, etc. Networks are trained and tested on a public brain tumor classification data set consisting of 3064 images and three tumor classes (meningioma, glioma and pituitary tumor). The thorough evaluation process revealed that the proposed CNN models can achieve competitive performances with regard to state-of-the-art methods in several scenarios. The best achieved accuracy benchmarks are 98.2% overall Dice similarity score and correct decision rate, and AUC values over 99.6% for each of the three tumor classes.