I use both. They are both correct. It depends what came before and what comes after.
This is how I use them:
If you are using option in your sentence, then I would say: I need to go shopping. I think the best option is to go shopping on Saturday afternoon because I haven �t got time in the morning.
On our trip we can visit the factory, or go shopping. I think the best option is going shopping, I �m not interested in factories.
The thing I like doing best on Saturday is going shopping.
I �m going shopping on Saturday.
I want to go shopping on Saturday.
I have to go shopping after work, so I can �t have coffee with you.
I �m going to go shopping....