Cough accompanied by too much phlegm (mucus)?
If smoking, asthma, chronic bronchitis, or emphysema are an issue speak with your GP.
Other than that, if you have phlegm issues you need an expectorant, so get something with guaifenesin in it. For the cough, any antitussive should work.
If you want a name brand try Mucinex DM which has both of what I just mentioned. It is a bit pricey but worth the money.

Disclaimer: This is not medical advice. Just a personal experience with said product.