Your first line of call is with the retailer. If they suggest that you deal with the manufacturer direct, then tell them that they are responsible. If it is best to use the manufacturer's facilities, then get (in writing) the retailer to declare that they have instructed you to do so. That will clear up any problems at a later stage, because if you go to the manufacturer direct, without the retailers's approval, then the retailer may refuse any further help or assistance.
Taking out an extended warranty is your choice, and you do not have to take it out straight away, there is by law a cooling off period. Some manufacturer's provide their own extended warranties, which might be better and cheaper that the retailers. You can also get extended warranties from the likes of Domestic and General, who service quite a number of manufacturer's products.
I know that you have suggested a computer or laptop, but I have had occasions were I have purchased printers etc, and the manufacturer have increased their warranty periods for free, on registration of the product.