What server do I need to handle 1000+ users simultaneously while they can post messages, upload pictures, and other similar stuff on a website based on PHP and mySQL?
You don’t need to handle 1,000 users simultaneously: you need to build something and ship it and start the process of discovering what you can build that will attract that many users. Seriously: don’t even start worrying about that kind of scale until you know you’re going to need it.
(That said, there’s no harm in keeping scaling issues in mind while you’re building the software—try to avoid making dumb architectural decisions that will be impossible to scale later. But deciding on your 1,000+ simultaneous user serving architecture before you’ve Built Something People Want is a huge waste of your time).