I am a british citizen (british born) and soon to be a US citizen, soon to marry an indian citizen. Would be better to apply for the k3 visa or should i call her on my british citizenship and let her travel on tourist visa while we apply for residency in US. We are trying to bring her over as soon as possible. I can call her over to UK in less than 2 months, where as it takes 6 months or more to the US. If i was to call her to UK on my citizenship, she would still hold indian passport, but with right to reside in UK. If i apply for k3 visa for US, can she still apply for tourist visa from the UK.

What would be the best way and quickest way.

The quickest way to what? What is your goal?

If your goal is to be together in the US, I think marrying in the UK will make things simpler all around. Marriage of Indian Citizens to foreigners, in India tends to be a complicated pain in the XXX Once married, and a USC, you can start the immigration process for your wife. However, you do not do so by applying for a K3 visa. You do it by petitioning for her to have the right to apply for a visa.

If you marry in the UK and she remains there, she can end up applying for the K3 visa in the UK. Her marriage to you will not change her ability to visit the US on an Indian passport.

I would like to add that once a petition is filed, the US consulate will not issue her a Tourist visa since she now would have immigrant intent and she will not be able to enter the US until she obtains her K1/K3 visa.

PS Citizens of India are not eligible to enter under VWP

Right. I should have said "will not improve". Filing a petition for a fiance or spouse visa will assure the non-issue of any visitor visa but not void an existing one. I suspect it is quite difficult for a single woman from India to secure a visitor visa to the USA anyway.