You dont need a server to connect computers; you need a way to forward/route packets. You can use a switch, router or basic computer to manage packets depending on what equipment you have a vailable. Once you have a way to route packets you need unique addresses for each of the machines you want to connect and routing rules to govern how the machines try to talk to each other.
For 10 computers, you need very little network equipment. All you need is a network switch. A 16 port switch will be adequate. If this network requires Internet access, you can plug the switch into an Internet router.
All of the computers on this network need to be running the same protocol, such as TCP/IP. If you have a consumer based router, it will include DHCP services thatwl configure the IP settings for your computers. If not, you will need to manually IP each host.
After about 10 PCs you should consider introducing a server and set up a domain to that you can centrally manage authentication and authorization services as well as other networking services.
Cheapest option: a wired/wireless router that has really good wireless coverage like the Amped wireless! ones. They are awesome. I have one of thier access points and they handle a lot of connections quite well. They have awesome throughput as well as HARDCORE COVERAGE! I love mine!!! ;-)
what you can do is get wireless USB adapters for those systems that are high powered (amped makes those too!) so you won't need to purchase a wired switch, as well as run cables. The amped wireleaa router is around 160 on amazon or newegg right now. You can get high powered usb adapters for around 40-60 bucks on newegg as well.
Best solution: a enterprise router, a wired switch and a wireless access point. I got the Amped Wireless AP20000G and it works well for the access point. Wired switches depend on weather you would want layer 3 mangement. routers vary from el cheapo 30 dollar ones to several thousand dollars.
To just connect 10 PCs you can use a HUB which has 10/10+ ports. But if you need internet connectivity and some advanced settings related to speed etc., buy a wireless router it will have some ports for PC connectivity and a port to the internet connection. This solves your requirement of creating a LAN with 10 pcs/laptops and you can have internet connectivity.