There are a lot of options to host Home Assistant, and I’m not going do discuss which is better, while just explain my choice: Raspberry Pi 4 (8 GB RAM Version).
I’ve started with a Raspberry Pi 3 and it was running HA pretty good, including many Automations, and many Integrations as well, like: Alexa, Mosquito MQTT, Zigbee2MQTTT, ESPHome, automatic Backup on Cloud, MotionEye, Samba Share, …
I like Raspberry because is small, low energy consumption (estimated: from idle 3.8 W to around 6.0 W with all 4 cores being busy) and simply enough powerful for my needs.
Recently I’ve anyway replaced the RPi3 with a RPi4, mainly due to lack of memory: RPi3 has only 1GB RAM, that became too low particularly using ESPHome addon which freeze and crash the system trying to compile and upload new firmware, unique solution was to switch off all the other plugins before using ESPHome.
RPi4 easily solve this problem, especially with the 8GB RAM version, the one I’m currently using.
If you want info about the migration process from RPi3 to RPi4, check this article: Migrating Home Assistant from Raspberry Pi 3 to Pi 4
As a useful reference, always save on your Favorites the Raspberry pinout, I’ve used it in many projects based on RPi GPIO.