The sentences "I don't mind. It should be quite interesting" mean that it doesn't matter to you, but you think that it will, for lack of a better word, interest you. To make the sentence smoother, you might insert an and or some other word to merge the sentences so that they are not so choppy. Also "it" refers to what you are talking about, so only you would know whether or not it is interesting. But based on the context of the sentence, I would believe that you have not yet tried it but believe that it would be interesting if you did try it.
I would not mind having a go at that, or as I would say it, I wouldn't mind having a go at that, means that you would like to try "that"; whatever someone is doing that you would like to have a go at or try.