I think your request is impossible. You want something cheap, easy and adaptable.
First, you have to create the program. I think remote controls work on a principle like morse or binary code (i.e. pulse on\off\long\short) so you have to interface with your IR device and learn how to read and write these pulses. Then you have to build a mechanism for learning and storing the data, an interface and finally, a way to send the data. While this isn't impossible or even particularly hard, it takes time and requires skill.
Second, you need a device with IR capabalities which works with LV. This is a problem. The cheapest would be a PDA, but that's not cheap and not good on battery consumption. You could use a computer, but you'd need an IR interface and you can't take it with you, so it isn't really a remote control, is it?
So, while it sounds like an interesting and fun project, I don't think you can do it cheap and easy. Why not use a real universal remote? I've heard of one you connect to the internet, tell it which devices you have and it downloads the codes by itself. Also, you can program it to synchronize. For example, when you press DVD, the DVD will turn on, the TV will switch to the right channel, the audio system will go to the proper mode and so on.
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