Designing a high performance LAN Party network that doesn't lag under pressure requires understanding several factors. I'll first discuss balancing bandwidth throughout the network.
If you're running a small LAN of less than 24 nodes (or ports or players) and don't expect to grow beyond that, a simple unmanaged 10/100 switch with 24 ports should handle your needs just fine. Many manufacturers (Linksys, Dell, HP, and others) provide inexpensive models that are plug-and-play, so shop around for a good price.
On the other hand, if you plan to expand beyond 24 players, your should definitely consider starting with switches that feature at least one Gigabit Ethernet (GigE) port in addition to the 24 10/100 ports. With less than 48 nodes, you can easily connect two table switches by a single Gigabit connection between the two 24-port switches and have great bandwidth between them.
These switches do not need to be managed since you will only be maintaining a single switch link. The nice thing about starting at this level of switch also provides for your later progression into the large LAN scenario I'll discuss next. This preserves your equipment investment!
TIP: While you're switch shopping, make sure any purchase candidates have enough bandwidth to handle full speed on all ports simultaneously. This is usually referred to as "non-blocking" in specifications, but it's a good idea to also check the switch's bandwidth or switching capacity spec to make sure the numbers add up. (The info you need is sometimes listed under "switch fabric", too.)
For a 24-port 10/100 Mbps switch at full duplex (100 Mbps both directions) the switch bandwidth specification should be at least 4.8 Gbps - 100 Mbps per port x 2 (transmit and receive) x 24 ports. Note that each 10/100 port adds 200 Mbps and each gigabit port adds 2 Gbps to the switch's bandwidth requirement. Make sure you add in bandwidth for dedicated uplink ports, which count just like normal ports.
If you can't find the spec for 10/100 standalone switches, don't sweat it, since it's unlikely you'll find any current-design products that aren't non-blocking. But make sure you check the spec for any gigabit gear you're considering. There are switches out there that say they're "non-blocking", but whose bandwidth numbers don't support the claim. For example, a 24 port gigabit switch should have 48 Gbps of bandwidth. Anything less, and you're not getting "non-blocking" performance.
Once you pass 48 seats, you need to start thinking BIG. While it is possible to purchase big switches with hundreds of ports on a single chassis, it's neither cheap nor practical for a large LAN Party network. For this reason you will be combining many table switches in a tree-like structure shown in Figure 1.
Figure 1: Basic LAN Party Network Topology
(click image to enlarge)
At the base of the tree you will find a piece of equipment commonly called a "core switch". The core switch is used to tie the rest of your network together with super-fast non-blocking all-gigabit performance. Gigabit Ethernet is necessary in the core switch to prevent data flow from being bogged down by dozens of 100 Mbps Ethernet clients.
Once you're connecting more than two tables and / or a server row switch, you're definitely to the point where you need to investigate managed solutions as well. If you've ever run a large LAN Party using all unmanaged switches, you will agree that locating a performance problem is almost impossible without shutting everything down and starting things up one at a time until you locate the problem. For your own sanity, be sure to pick a good managed gigabit switch for your core. I'll have some recommendations for you shortly.