I am right to think; that if you are a company you dont have to pay VAT/or can claim it back?
No. If you are VAT registered then you can reclaim VAT on purchases. There is one instance that I can think of where you wouldn't pay the VAT - EU acquisitions where the VAT is zero rated and accounted for in your own member state.
If so, how's this work? Is what I buy gotta be for the company (obviously right?) but how do I get this status if this is right - or just a rumour?
Yes it has to be for business use though there are some instances where you might purchase something for business and personal use. You can then reclaim a percentage of the VAT depending on the percentage of business use.
To get this status you simply have to voluntarily register your business for VAT but voluntary registration is only sensible in certain circumstances.
Why are you asking?