A mosquito is so small that even 1:1 -- working at the minimum focusing distance for a dedicated macro lens -- will give you a pretty small image. 1:1 means that the object size is the same as the image size on the sensor. For mosquitos (I have never tried one), you would either have to crop severely or use a lot of extension to get better than 1:1. For illustration, I will post a larger version of my avatar below. This was shot with a macro lens with enough extension (using tubes) to get more than 2:1, that is, more than twice the magnification of the lens alone. This spider was not all that big, but a lot bigger than a mosquito.
Macro is a specialized type of photography that is very demanding. My suggestion is that you spend some time trying it, and reading about it on macro forums, etc.--before you invest a great deal.
For bugs, 100mm or close to it is a pretty comm length on a crop sensor camera, although you still have to get quite close. It's what I use for bugs. You can use a 60mm, but you have to get very close with it, and you will have a lot more frustration.