Reach out to IT service providers like myself if you need help with deployment. Standardizing on all your servers and desktops will be a great help. Uninstalling LogMeIn is a nightmare, since you need an admin username and password for each machine before you can run a script on it. Domains are much easier but lone wolves and workgroups are a major chore. Get this done first before attempting to launch your migration. Documentation is VERY important, especially of usernames and passwords where needed. Once you're on ScreenConnect, will help with this.
Get good on scripting for functionality. Much can be done via the Tools function of ScreenConnect - but it will be a mixture of PowerShell/DOS and a little Linux shell.