Advice from a guy who's gone through this a few times:
1. Monitor your retention. Are people coming back or just checking your site out once? You can go viral very quickly but tank just as quickly once the initial interest dies down.
2. Start thinking about a business model. Highly viral sites that don't retain well could really hurt your bank account if you're not monetizing. If you can't can come up with an interesting one, throw up some ads to tide you over.
3. As soon as possible, get your database on dedicated hardware. Your bottleneck is going to be the database: so memcache, add the right db indexes (get a backup db so you can hot-swap while you do this), and add lots of RAM if needed. You don't want to be scrambling to migrate your database once you hit the limit.