Hi,
I think you already know the answer to this as you spent the most time on the third option and you are correct. The Internet is awash with too much information for buyers, they have information overload. So you should concentrate on niche websites for 2 reasons. The first being ease of use for the customer, finding what they want to buy in seconds not hours, the second is SEO, your sites can interlink and if built right pass on link juice and customers by promoting your other sites on each other. You will rank much easier with a keyword domain combined with keyword content. I am doing exactly this at the moment within a number of niches globally and have a team of expert developers, content writers and SEO experts working under my direction and it is working really well. You will need to build a mini-net around your money sites and build links to them, just make sure there is no pattern, then build links from your money sites to each other from keywords not banners and you should rank really high on Google.

I would think #3 is the hardest to execute and takes the longest time. Amazon will be quick and reach to a larger audience instantly. I'll combine #1 and #3.

Considering the three key strengths you have ( Clothing experience, Access to multiple brands and physical outlets), and the specifics of Argentina's online retail space, I'd go with option 2. Gilt does have a unique brand image and you can develop something that has more sustainable competitive edge. Trying to be a mix of all things for everyone will put you in competition with someone like Mercado Libre and also strain your focus. Many of the other themes and products you mention fit under the 'Lifestyle' category and those will be a logical extension once you establish yourself as a good focussed fashion/clothing online retailer. All the cross-reference and sub-sites style architecture creates great business for those in the business of search engine optimization and generating clicks but there is little evidence that such a model does indeed create a higher margin or higher volume of business. The benefit for investing in a focussed brand for online retail is that it tends to generate a higher order of repeat business and that is something worth considering in a country like Argentina where the internet retail business has a significantly higher level of penetration when compared to many other countries. The business of promoting a web of online properties is a complicated exercise that sounds very exciting but it is not necessarily the best way to establish your online presence. You have physical multi-brand retail outlets and I'd lean towards a hybrid online presence model that will use the online presence for brand building and the store as well as related supply chain for operations. Again, the answer lies in the details for what you want to accomplish first with the online business - You want Scale, or Margins, or Sustainable business based on branding or just skim the market for whatever opportunities exist?