To get some quick Beta users for your web app, you should make a pre-launch contest. Distribute on social media for fast exposure. Build Buzz with it. Hold on to that buzz for a while.
Give some premium accounts as prizes. That way, you will have first-hand customers who will test the app for you and give you feedback. Since they won the whole thing they will be excited about communicating with you.
I did this for my startup and it was incredible. Probably the coolest social media campaign I’d ever done. The results were far above my expectations. If you want more info about this, I’ll be happy to share the details here.