Aside from having ads on the site, your only real option is a paid plan. In that case, just start marketing the project as "beta" and add a pricing page that says the pricing is "coming soon". Continue building out features and once you get a good enough product to charge for add a paid plan and flip everybody else over to the default "Free Plan" that's limited in a way that users can still use the site, but have enough reasons to upgrade to the paid plan.

Whatever you do I'd try to listen to your users and see exactly what they want. 3,000 users really isn't very many and it would be really easy for them to disappear. Talk to your users, find out why they're using your site/service, keep that in mind when building out your feature set.

Edit: Keep in mind, building out the service and keeping it free is also an option, especially if you enjoy working on and running the site. If you listen to your users and keep improving the product, it's very possible to turn 3K monthly users into 300K. I run an API that has a front end site which gets around 175K monthly hits and brings in about $1300+ (CAD) a month from the ads. The site costs peanuts to run so I'm happy to serve the 35 million API calls for free and fund the project 100% via adsense. It just depends on how far you'd like to scale it and what your users are like.