What is your budget and what do you want to do? And do you want to do everything yourself or do you want support?
You haven't mentioned AV and one of the biggest benefits of an HA system is having it control your AV.
I have Control4 and you can integrate BI into C4. There is a basic BI driver that is free that lets you integrate all of your BI cameras into your C4 system and there is a more advanced driver that lets you create hot zones that do actions when you click on them. For example, let's say you have a fixed camera in BI in a room that displays a light and a fireplace. You could set it up to turn on the light or fireplace when you click on it. But cameras are a small fraction of all of the fun things that you can do in a HA system.
Control4 is not cheap, but it is cheaper than some of the dealer-sold alternatives like Crestron, and all hardware in C4 must be added by a dealer so it is not a fully DIY system. You can do pretty much all of the programming yourself, after hardware is added by your dealer. C4 is quite good for whole house audio and video distribution plus lighting, security, door locks, doorbell, window blinds, HVAC, pool, etc. It can control your AV devices via IR, IP or serial interfaces. High end systems will have matrix amplifiers driving speakers in each room and video matrix switches allowing any video source to be sent to any room. Centralized video is very expensive - but getting cheaper with new technology like Video Storm Net Play. In an ideal world you have lots of cabling in your house, including multiple LAN drops to each room that has AV equipment, ceiling speakers in each room, HDMI cables to each room, etc. You should think about the cabling that you want before your house is built. Also think about whether you want AV devices local in each room or do you want them hidden away somewhere.
C4 integrates well with most things out there today including Amazon Alexa. And everything in the system can be used to control everything else - so I use security system motion sensors to turn on lights. You can have a "Good night" routine that will turn of all lights, arm your alarm system, turn off all audio/video in the house, etc. And you could activate that Good Night scene from a voice command with Alexa, a button by your bed, a C4 remote control or an app on your phone. Amazon Alexa is WAY more useful when you can use it for HA, like turning lights on/off, closing blinds, locking doors, etc.
But a typical system would probably start at around $10k and go up from there. A bare minimum system would probably start at around $2-3K - that would get you an EA-3 controller, a remote control and a bit of work from your dealer for setup.