What wwouldn't be a problem. Depends on the way it's programed and stuff like that but the 10$ version should run this just fine : )

My $20 wordpress site handled 4000 uniques a day and 6000 pageloads. I would imagine the $10 plan could handle 300 like a breeze. Setup cloudflare's free version after you get it all going and W3 total cache and you would be good to go.

You can get the initial droplet setup with LAMP and install wordpress all using the droplets IP address... then export/import the wordpress content and copy your theme over and finally update DNS to send traffic to the new server.. there should ne 0 downtime in this process, I just did it yesterday on my major website.

@danafrancey do you did any optimizations on your server? 4000 is a lot even for a 2GB server