To run an IRC server or any IRC-related services, your VPS provider must allow IRC in their Terms of Service, otherwise you run a strong risk of being shut down as soon as they discover that you're running IRC services on your VPS. In general, a VPS that allows IRC is more expensive than a VPS that does not allow it, since this is more of a specialized type of service and requires more resources from the network provider due to IRC-related services being more frequently a target of network attacks.
However, all is not lost, you can still find a low cost IRC VPS that will fit your needs. Luckily, most IRC services do not require much server resources (disk space, RAM, or bandwidth) compared to many other types of hosting, so you won't need a large VPS unless you are doing some major things on IRC, which the majority of us are not and are just wanting to host some chat bots or a small IRCd server.
If you are looking to run an IRCd server or eggdrop bot, then you will want to get yourself a Linux VPS, otherwise if you are looking to host a script or bot that runs on mIRC (mSL), then you'll want to look into a Windows VPS. In both cases, you will probably be fine with just 128MB of RAM and a few GB of disk space, but it just depends on what you're wanting to run. Almost all IRC VPS providers will allow you to upgrade the VPS at any time though, so it's usually best to start small and then upgrade if you find out you're low on resources. If you want to prevent any potential problems though, you might consider upgrading the RAM to 256MB just to be safe and give some extra breathing room.
If you're looking for a great IRC VPS provider that has reliable services, low prices, and outstanding customer support, then we highly recommend checking out http://www.XygenHosting.com!