I need it basically to convert videos etc. Another thing is I need to use a 64 bit Linux OS on it. Also Can I install a 32 bit OS on to a 64 bit system?
I don't have a specific budget but a Motherboard and CPU together within 8000 would be a okay for me.
Yes, you can use a 32-bit OS on a 64-bit hardware system.
An AMD X2 7750+ processor at around 3.5k should fall within your budget. There's a wide range of motherboards to choose from. Since you didn't mention gaming, I assume that's not on your priority list.
If you want to be able to download video files from a DV camera, an onboard Firewire (IEEE1394) will come in handy. The MSI K9N2GM-FIH is one such motherboard and will cost 4-4.5k. It has an NVidia 8200 graphics onboard. I also suggest at least 2GB RAM.