Having a putting green at home will inevitably improve your short game; many professionals have their own putting greens.
If you have a real grass putting green, you have to be prepared to put in the time maintaining it. Cutting to 3/16 of an inch every one to three days is only part of it. Allow an hour a day for adequate maintenance. If you do not have the time to do this, or do not want to, consider employing a professional firm to fit a synthetic green instead. Although hole positions will be fixed and it may look artificial, the playability of the surfaces in recent years has become excellent and the need for maintenance is eliminated. This option will, however, be more expensive than the real grass option.