I don't like PuTTY either, but its terminal emulation has always worked better than anything else for me. I have not installed Windows 10 yet, so the new WSL stuff might work better.
If you only have a few machines to manage, use the PuTTY dialog to create and save a config for each machine, then install
Cmder and create
Settings|Startup|Tasks to assign hotkeys to launch each config with the command "Putty.exe -load <machine-config>."
If you also use ssh-keys, you'll never even see the PuTTY dialog again unless you need to add a new config. Use ssh-keygen to create them, then import them into PuTTYGen to translate the private key into PuTTY's format and save it as
putty.ppk. Keep the original key files in case you find a way to dump PuTTY and switch to ssh later on.
Add a shortcut to your Windows Startup folder that runs ""C:\Program Files\PuTTY\pageant.exe" "C:\Users\
<user>\.ssh\putty.ppk"". When you log in, it will ask for the password to decrypt the private key. Run Cmder and enter the hotkey to log into each machine with a working terminal.
I hate that it's non-standard but the terminal works very well. If you find something that works for you, please come back and report what you did so I can copy it.