Here are some of my suggestions. Since you have a dataset consisting of two columns [Text, topic_labels], and Topic_labels are of 6 categories for ex: [plants,animals,birds,insects etc] only. This is a relatively small task. I recommend you choose the model that focuses on accuracy, rather than speed and memory. Accuracy is defined as follows.

TP, FP, TN, FN denote true positive, false positive, true negative, and false negative.
I recommend the models stated in this paper. In general there are two categories:
- Rule-based methods. Rule-based methods classify text into different categories using a set of pre-defined rules, and require a deep
domain knowledge like linguistic. Rule-based approaches classify text into organized groups by using a set of linguistic rules. One of the most successful rule-based algorithms in Topic classification is transformation-based learning (TBL).
- Machine learning (data-driven) based methods
Since you mentioned deep learning, you want the second category. In the second category, an accurate method is the Feed-forward networks. Even though they are quite simple, they have achieved high
accuracy on many Text-classication (or Topic-classication if you will) benchmarks.
Feed-forward networks view text as a bag of words. For each word, they
learn a vector representation using an embedding model such as
word2vec or Glove, take the vector sum or average of the embeddings as
the representation of the text, pass it through one or more
feed-forward layers, known as Multi-Layer Perceptrons (MLPs), and then
perform classification on the final layer’s representation using a
classifier such as logistic regression, Naïve Bayes, or SVM.
However, if you want more fancy ones, and the latest state-of-the-art one, you can read the following table.

The most accurate one is XLNet-Large (ensemble) among all the instances in the benchmarking.