Yes, wasp only connects to goshimmer nodes. Hornet & Bee are for the mainnet NOT development. Wasp has a really straightforward readme to build. Yes
wasp-cli is how you currently interact with smart-contracts NFTs, etc.
I had some trouble with the docker image for goshimmer to work so I recommend just building the goshimmer node on whichever computer you are going to be messing with wasp. Wasp by default looks for localhost for the goshimmer node.
Build a go shimmer node
Simply clone the develop repo to your
git clone https://github.com/iotaledger/goshimmer.git
Then the thing you want to run is in
build_goshimmer_rocksdb_builtin.sh. To build you just,
goshimmer command will show up in the directory that you can execute. Here is a systemd service example if you want to make it a daemon service:
If you are running arch-linux there already exists a supported go-shimmer repo in the aur and all you have to do is run
yay -S goshimmer-bin
You have a second topic that is harder to answer, how to start a private tangle. Not enough information to answer this (do you want a goshimmer private net or a private mainnet), make another post.
See the goshimmer docs: