I am thinking about having employees use a remote desktop connection to connect to the server running windows server 2008 r2 to access programs and run programs from the server. The majority of their work and time would be running on the actual server through the RDC. The number of clients would be somewhere around 10-15 total. I do plan on Installing some form of Anti-virus software however, I am skeptical as to whether or not I should allow users to browse the internet on the main server computer but I don't have any other logical alternatives besides having them minimize the remote session and browse on their client PC. The question is whether or not it is recommended, or safe to browse the web on the server? I know that I could allow only certain websites that are trusted but I don't want to jump into limiting employees to 10 total websites right away. If it is not recommended to use the server for web browsing what kind of alternative can I use to allow them free-range access to browse the web?
This is my opinion, but you should never be browsing the web from a server.
Can you? Yeah. Should you? Absolutely not.
If you want a proper set up for your users, you want to plan out either a virtual desktop infrastructure, or a RemoteApp deployment.
As @HopelessN00b stated, browsing the internet from a server is about as safe/risky as doing it from a client workstation. The difference being that the scope of impact of a malware infection, hack, etc. is potentially much greater on the server. That being said, you are running an RDS server whose purpose is to host user sessions and run user applications. Users browse the internet. Asking them to minimize their RDS session every time they need to browse the internet strikes me as inefficient and may impact their productivity if they need to browse the internet as part of their job or business process(es). Many users us web based tools and applications as more and more vendors put their applications "in the cloud" (QuickBooks Online being just one example).
My recommendation would be to sufficiently secure the server (AV software, user and software restrictions, etc.) and make sure you're backing it up completely and regularly.