It really depends on how you want it sound. A lot of can usually be exchanged with many (vice versa) more than much. Such as saying "There are many puppies" you could say "there are a lot of puppies" it really depends on which one you want to say and the context of the sentence.

'A lot of' and 'lots of' are informal equivalents of 'much' and 'many'. They are also easier to use than 'much' and 'many', because you can use them with BOTH countable and uncountable nouns. Many people Much money A lot of people/ a lot of money In everyday speech and informal writing, it is very normal to use 'a lot of' or 'lots of' rather than 'much' or 'many'. In fact, it isn't natural to use 'much' in positive statements. No native English speaker these days would say 'We have much time'. This is correct, but very unnatural-sounding. In most cases, we would say 'We have a lot of time', or 'We have lots of time'. The only situations where you wouldn't use 'a lot of' or 'lots of' is in formal speech and writing, for example in business letters. These expressions would be seen as too informal for these contexts.

many = for countable nouns much = for uncountable nouns a lot of = can be used with both types

This post has a few good examples: http://www.italki.com/question/303533