So you're moving to the US and want recommendations on who to use. There will be plenty of threads on the topic, but here are some of the basics.
Who ever you use in the UK, ask them who gets sub-contracted on the US side and when you have a name, to check them out against the moving scam site.
 Questions to ask:
Ask what exactly is covered in the quote:
- Does it include packing, loading and the reverse as well as clearing out that packing material?
- Is there storage included at either end if needed?
- Can you track your container?
- What do they do about x-ray/inspection charges?
- What does the insurance cover?
None of the following companies are endorsed, they have just been mentioned in previous threads for your convenience, it is also not an exhaustive list either but a starting point:
 Additional Notes:
- Any quote where the company hasn't sent someone to check your contents is probably going to be unreliable.
- Asking for recommendations will only useful if you say where in the US you intend to move to and where you are coming from, as well as if you expect a full container or a shared container.
- Quotes can range from £1500-15000 depending on level of service, location and speed and can take anywhere from 4-16 weeks, but 6-10 weeks seem to be the norm.
- For smaller items you might want to consider air freight or using pallets, some info can be found here.
- Some shipping companies will send a small amount of boxes for a smaller fee.
- Many shipping companies will price match so do get quotes from various places before you commit.
- Fitshipper Helps you search which US service offer the best rate to ship parcels based on size/weight around the US and internationally.