I had a similar use case (SMS/text verification for phone number based login) and I just started using Plivo (https://www.plivo.com) for this. Until now it works great.
Plivo is similar to Twilio but in my case (Netherlands market) it was just a bit cheaper to send local/domestic text/SMS messages: $0.06 for Plivo vs. $0.10 for Twilio.
Starting out is very simple, you get $5 free credits which (in my case) let me send something like 80 free SMS messages, which was plenty for my testing/development.
I’m not using their SDKs but their REST API, which is very easy to use.
All in all works great - fast, cheap and easy.