What visa should we apply for?
You will need to submit the I-130 for your spouse. Whether this can be done through the DHS unit at the Embassy in London is dependent upon how long you have been in the UK up to that point.
Is it called the Immigrant Visa for a Spouse (IR1 or CR1)?
As you will only have been married for six months it will be the CR1 which means that you will have to 'remove the conditions' just prior to two years after entry on the visa.
How long does it take?
Depends on whether you are eligible to file in the UK or whether you will have to file in the US. If the latter then you can expect to be waiting anywhere from between 8-12 months for the actual visa to be issued. The former can vary between 4-6 months, roughly. These times are just guidelines and should not be taken as gospel.
If it takes more than a year, can my British spouse stay with his family in the US on any other kind of visa while we wait for the one above?
The VWP can be used, if he is eligible for it, to visit in the interim but it is for visiting alone and is for a maximum of 90 days at a time.
The links in my signature, below, should be a starting point for you if you are intending for your spouse to immigrate.
Other forums you may find helpful are visajourney.com, (which has guides and timelines) diveintoamerica.com and britishexpats.com.