(Disclaimer: I'm on iOS)
After having just tried and hated severaI of the side-number, masking or burner apps like Hushed, Sideline, Burner etc, I was getting really frustrated because I couldn't find anything that did what I wanted, which was:
What I did not need:
That's when I randomly stumbled upon TextNow. Their text service is 100% free, matches all of the above, and (while they don't make claims about privacy) I found it to be more "secure" than any other service I looked at. Most of this is due to their having a web app, which, according to their privacy policy, will track only IP, Browser, referrer/exit, date and time, typical cookies/third party cookies and web beacons that let them know which emails you open.
As far as I can tell they do not retain copies of the texts you send via the web app, but they DO retain copies of the SMS messages you send via the phone app. You probably shouldn't use a service like this for sensitive information, but if you do, I highly recommend using the web app only. This is what I do, because the phone app also captures your phone number and wireless carrier, which is far more identifying than IP.
Anyway, this worked for me. All without needing to jump through the truly ridiculous hoops the more popular apps are asking, OR pay $5 to $30 just so I don't have to give my real number to something for five seconds.