|Ok, you don't "physically" connect wireless computers. You connect wirelessly.|
First and foremost, I would NOT use a wireless solution in this situation. It's insecure and wireless has inherent issues with lag and latency. But mostly I wouldn't do it for security reasons.
Now having said that....
First, configure your Wireless LAN (WLAN) on the SOHO Router. I recommend using WPA-2 Encryption and a complex password.
Once you have the WLAN setup, then you connect your wireless clients to it.
As for accessing applications on the server...........
You need to understand that in a direct comparison between wired and wireless solutions, wireless sucks.............really bad! If you plan on running network applications across wireless links you're going to find things slow and boggy. At the very least, I would have the server plugged directly into the router with a network cable since it's going to be handling multiple connections from multiple clients at the same time.
I would test and compare a wired client to a wireless one and see if the performance of the wireless is merely a little slow and annoying, or if it's unusable (a distinct possibility).
As to what router to buy, that depends. If 5 people give you an answer, you're likely to get 5 different make/model of router.
Personally, I would go with all Wireless N equipment (router and NIC's on clients). Other than that I can tell you I've liked the Linksys (Cisco) products I've worked with more than any other.
I will repeat one last time, I would go with a wired solution in this case since it's a medical clinic accessing personal and private medical records for patients. With wireless it's not a problem to hack it and even WPA-2 encryption can be cracked given enough time and CPU cycles. With a wired network, a hacker can't just sit outside your office and hack you, they'd have to physically plug in.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.