@Ketan, Get a server with SBS on it, and you will have Remote Web Workplace, and you will not have to worry about LogMeIn or RDP, etc.
@Barbara, Wendell gave you a pretty good run down. I'll add a few more. First, if you are setting up now, then get a serve and a server OS. You can only do about 250 more things with a server. Besides the fact that pound for pound, it will always be faster, more reliable and more secure than any desktop.
Part of what is nice about a server with Microsoft is what is termed Active Directory. Active Directory ties together all of the users and computers along with Group Policy to allow a myriad of advantages.
One of the keys of a server is that your employees don't log into THEIR individual computer, they log into the server. Once they enter their username and password, the server authenticates them and says, "Yes, this is Barbara, and she can access the server and AC and whatever else. Of course, the admin told me not to let her see those accounting files."
Permissions and sharing are much more powerful on a server and its OS than with a workstation. And, it's much easier to add and delete users, add and delete their passwords, etc. You never run the risk of someone losing their password as you can set it. Also, when you set up users, you can give them certain group privilegs such as admin, power user, or just domain user. These automatically come with certain permissions. Servers can allow things such as mail servers, typically Exchange Server if Microsoft. You host your own mail and can also send intraoffice email that is therefore HIPAA compliant.
One of the most beneficial things of a server is what is called Group Policy. There are hundreds of group policies. For instance, you can lock down the desktop wallpaper or sizing so they don't add their kids to their desktop. You can set the type before the screensaver. You can set whether or not it locks on the screensaver. You can delete Control Panel or the Start Button or whatever. You can also do Group Policy for groups. For instance, you could put all of the front staff in a group and all of the MAs and clinicians in a group and give them certain permissions.
I could go on and on. With peer-to-peer, the desktop that holds that database is no different than the others. With a server, it controls the network via the domain. The domain is a POWERFUL concept that can't be duplicated on a workstation. The networking of computers is based on unique protocols of each computer consisting of IP addresses, subnets, default gateways and DNS. These can be set statically as on a peer-to-peer, but the server manages all the computers via DHCP. So, in general, nothing goes wrong. Now a router can use DHCP, it just isn't as good
I would highly recommend getting a server if you can control it. Not to mention the increased capacity to run RAID, etc.