To answer PP's visa questions.
Assuming he is an American citizen and you are a British citizen? Are you married or planning to become married? Without that you can't get a visa easily to go and live over there. There's a spousal visa and a fiance visa. If you are not married yet, the spousal visa is a better option because you'll be able to work and travel in and out of the US as soon as you enter because you immediately get a green card (it's also slightly cheaper in terms of fees).
With the fiance visa you will have to get married within 90 days of arrival in the USA and then you apply for the greencard. This option means you won't be able to work for several months (up to 8/9 months under current waiting times), nor leave the USA without abandoning the whole process and having to start all over if you wanted to come back to the USA.
If your other half is an American citizen and has live in the USA for at least five years as a citizen, including two years after the age of 14, then your baby is automatically a US citizen too, so they don't need a visa just apply for their American passport.
Cost for your visa if you go for the spousal visa:
Initial application: $535
Entry fee: $220
Visa Medical fee: £290.00 (they make you do this at only one specified doctors office in London so you have to travel to London to get this done)
You also have to travel to London to get your visa approved so factor that into the finances.
Your husband will have to provide financial information to show he can cover your costs - for a family of three he needs to show he will be earning $28,787 in the USA. Or if you have assets like savings from the sale of a house it must come to 3x the amount above. He can use a family member as a joint sponsor if he can't meet the financial requirement.
Also, none of this is going to be quick - current waiting times to process a spousal visa are anything from 12-18 months.