You can run a transcription model and a language model (the AI you talk to) locally however you will need a beefy GPU especially if you want to run the large models for better results.
OpenAI’s Whisper is open source and does transcription, and you can run inference on language models like LLaMa (+variants) or GPT4all locally. To store information long term (“AI memory”) you could find an open source vector database but I don’t have experience with this.
LLaMa-2 was just released and the fine-tunings people have made of it are topping the leaderboards right now in terms of performance for an open source language model. As for inference, don’t forget to look into quantization so you can run larger models on limited vram. I’ve heard about vLLM and llama.cpp and its derivatives.
If you’re looking for a GPU ~$300, I heard a used 3060 is better value than a 4060 right now on performance and memory throughout but not power efficiency (if you want an easy time with ML unfortunately the only option is nvidia).
Good luck! Would be nice to get an update if you find a good solution, it seems could share your use case