Via an App:
There are plenty of apps out there to allow you to send texts from your own phone number via your computer. All of these apps work exclusively on Android.
For a comparison of these: http://www.guidingtech.com/33996/mightytext-vs-pushbullet-vs-airdroid/
If you’re looking for another number. Google Voice can provide that, and offers compatibility with iPhone
Of course. If you have an iPhone and a Mac. You can use imessage.
Did you know each carrier has its own email address? Of course, this presumes you know the carrier.
For short messages, up to 160 characters, use the SMS email
For messages longer than 160, use the MMS email
Keep in mind, you can’t send anything complex, as it will come into the receiving end’s messaging app. And this may or may not work with iPhones.