If you have a limited budget for the online advertising of a well known brand, will you go for Google Adwards (quality)?

It actually depends on the objective you wish to achieve. However, having said that, for a well known brand, Google Adwords makes more sense as it is Intent based marketing, whereas specialized websites will give you reach, but not a higher conversion rate. 

Yes you will advertise with limited budget.

advertising on google adwards or youtube is kind of expensive, there are lots of other websites offers campaigns on minimum budget down to10$ or even5$ no matter what product or market you choose.

no one can give you a good answer without getting full details, brand, product, market, etc.