How to translate "I go to do something"
 

Hi there!
I've studied two forms to translate "I go to do something":
1) Base1 + ni+ iku
2) Te-Base + iku

Examples:
1) watashi wa kasa wo kai ni iku
1) watashi wa kasa wo katte iku

Is there some difference between form 1) and form 2)?

There's not really a big difference. The first one is like "going to do x" and the second one is "go and do x." They both mean pretty much the same thing.

I do read a difference.

1) watashi wa kasa wo kai ni iku

I will go to buy an umbrella.


2) watashi wa kasa wo katte iku


I will buy an umbrella and go.

Mind I am not as expert as the 2 persons before me...
However the way I see it, is the に gives me an idea of purpose, while the て form gives more an idea of one action following the other.
I am not English native, but I think it can be equal to "go in order to buy" and "go and buy".

Basically...use them as if they have the same meaning :)

As MMM pointed it out, there is a rather large difference in the meanings. The two sentences will NEVER be interchangeable.

With the first sentence, the speaker's purpose in going out is to buy un umbrella. His destination is a place where umbrellas are sold.

With the second sentence, however, the speaker's destination is someplace else. He just intends to buy an umbrella on his way to his destination for whatever reason.

In my opinion, #2 sounds like buying the umbrella is a secondary objective, something you'll do after you've gone. Am I totally wrong?

Think of it as a series of events. First I will but the umbrella, then I will go. Or "I will buy the umbrella in order to be able to go". It sounds to me like the going is dependent or will be assisted by the purchase of the umbrella.

That makes a lot of sense. Thank you!

Wow that confused me alot :) Let me use another example:
家にパンを持っていく I have always thought this meant I grab the bread and bring it home. To get the meaning I wanted should I say 持ちにいく? What is the real meaning of 持っていく then?

hy OP, I'm from Rome ^o^