Here's what I did:
My feeds run on an HP T5730 thin client. The T5730 has a 1 GHz AMD Sempron 2100 processor and 2 GB of memory. The OS is Windows XP, and my feed software is RadioFeed. The only logging I do is the RadioFeed source client logging. CPU utilization for my two feeds runs between 2% and 15%, so it should be able to handle four feeds just fine. The client runs 24/7, and it is automatically rebooted by a scheduled task once per week.
I chose the thin client because the processing power needed for a feed is relatively minimal and because the thin client, being fanless, consumes less than 20 watts of electricity as configured from the factory. The client originally came with a 1 GB flash memory hard drive; I removed it and slightly modified the client for a used 50 GB laptop hard drive. The hard drive bumps up power consumption only slightly.
The client runs two instances of RadioFeed, one for each feed.
The audio from the scanners is fed to the thin client through a Behringer UCA202 USB audio interface. One interface can be used for two separate feeds because the interface has separate left-right channels. The feeds in my sig come from the 5730. I also use a compressor/limiter/gate on my feeds to help level the audio level, but that's just my preference.
The client has performed great for over a year now. I use Windows Remote Desktop to access the client's desktop whenever needed.
There are newer clients available used on eBay that have more processing power, but this one does great and is available rather cheap (less than $50 if you shop eBay carefully).
Searching these forums for
thin client feed will turn up a number of helpful threads.
Let me know if you have any questions!