It's about 6 years since we left Moscow, but I don't suppose things have changed that much, so I will try and help.
Firstly, if you are only being offered the job and no expat package you need to be wary. Rentals in Moscow are a ridiculous price for anything better than old soviet style accommodation. $250 000 dollars a year is not unusual.
Unless you live in central Moscow, you may well need a driver. DH drove himself, I didn't.The traffic is worse than anything you will ever have experienced and the police stop and fine you for no reason in particular. They and all other institutions are endemically corrupt.
You will need some sort of private healthcare provision.
You will need to pay for private schooling for your eldest. International schools are thin on the ground, expensive and can involve a long commute as they tend to be out of the city centre.
You can buy anything you need in Moscow, but many supermarkets made me weep. There is Stockmann's, a scandinavian supermarket, but again that is expensive.
Russian society is not easy to break into. Once you know Russians they are wonderful people, but on a day to day basis Russian society can be quite oppressive for foreigners. You will need to work to meet other expat mums through school or the British Women's Club.
You will want to make regular trips out of Russia, especially in the winter. You need to cost this too. The weather is bearable as the built environment and cars etc are all geared up to deal with this. Nobody ever switches off their heating in winter and cars are built to deal with temps of -40c.
You will need to learn at least some Russian.
For people of colour, life can be trickier. You just need to be careful. Having said that I have an Indian friend who has lived in Moscow for 20years without problems, but the Korean companies forbade their employees from using the metro for personal safety reasons.
I'm not saying don't go, but I don't think this is a decision you should make in a rush before you have investigated housing, schools etc. DH worked for his long term employer whilst we were there, so we still had all the same T's & C's, - not sure how it would be working for a Russian company. The culture is very different.
Moscow is not an easy place to live. I was glad when we left and went back to Dubai, but I do know people who loved it.
Good Luck