First time coloring my hair - need suggestions?

Hi ladies,

I have never colored my hair in 30 years of my life. But finally now my greys are getting visible and its kinda pulling down my confidence.

I've long waist length hair dark black with natural brown undertones under the sun. I already have hairfall and hair thinning and i am worried that coloring them the wrong way will lead to even more hairfall (abhi toh meri shaadi bhi nahi hui hai 😭)

I want suggestions from the ladies on what would be the best way to go about for a first time. I want to hide my grey hair and also have a dark brown/mocha/chocolate colors. I want to kind of change the way my hair looks.

I am based out of Andheri, Mumbai. Any good salon recommendations would be appreciated and any tips too.

TIA.