Yes you can use DO for anything you want, not depending on number of visitors.
Concurrent number of visitors is important for selecting Droplet size. If you have a lot visitors in same time you could be in need of bigger Droplet.
You can se available Droplet sizes at Pricing page.
About optimization, that depends on your application.
For Web applications you can pay attention to caching. It will take off load from your server.
There are [Apache tutorial](Ihttps://www.digitalocean.com/community/tutorials/how-to-configure-apache-content-caching-on-ubuntu-14-04) and Nginx one.
If you have tons of images, do some image optimization.
For Nginx, there is also optimization guide.
Next depends on your application. For example if you use WordPress you want to pay attention for installed plug-ins so it doesn’t slow your installation.
Free feel to ask if you have more questions. =]
Nginx is a fast and lightweight alternative to the sometimes overbearing Apache 2. However, Nginx just like any kind of server or software must be tuned to help attain optimal performance. Here's how to optimize Nginx configuration.