General "shipping of stuff" question for the big move!

Just looking to get some info on what people have paid to move their stuff from the US to the UK.  I have gotten some general estimates, but they seem to vary quite a bit.  Honestly, I own very little.  Most of what I own could fit in my luggage.  My kids, however, are a different story.  90% of what I will be moving to the UK is kids stuff.  It isn't a lot and only about 4 pieces of small child-size furniture. 
I have lived in the UK before, but didn't take much with me.  This time I will be moving permanently, so I plan on taking it all with me. 
Any information you can give me would be very helpful.  Please share your experiences with me
And one more similar question is about plug converters.  I have very few electrical things I will be bringing with (for obvious reasons), but my kids have a couple of small lamps I would like to bring to make them feel more at home and a couple of other things.  What is the difference in converters?  I cannot figure it out and I want to make sure I buy the right thing.
I feel so clueless about so many simple things.   

I am using UPakWeShip and was quoted up to 30 cu ft for $550.  I'm only at about 16 boxes and 22 cu ft, so it's a lot of space!  Your quote will vary based on what you choose (door-to-door, door-to-port, port-to-port, etc), but I've found the folks at UPak really nice.  I actually just got off the phone with Chris and he was really nice to talk to and willing to answer all questions you have...even the stupid little ones.

I don't know about the lamps. Can you find similar lamps on eBay UK or Amazon UK?  Or possibly get them re-wired? 

Thanks for the response!  I haven't been on here much due to holiday craziness!  I actually just got in touch with the upackweship people and I am hoping that they are as good as they sound.  I have a few small pieces of furniture and the rest is boxes.  I am lousy at estimating size and such.  I just don't want it to cost over $1000 for me to move my few measly possessions.  I am thinking I can do it.  Your move date is pretty close to when I will be moving back.  I think we are looking at the first week in February, so I have to get this stuff figured out fast!  I am a bit stressed!!!!

Measure length x width x height in inches and then divide by 1728 to get how many cubic feet something takes up

Thank you!!!!!  That helps a lot!!!!!  I am so clueless.  lol

No problem! I had to google how to figure out cubic feet since I had no idea when I was asked how much cubic feet I needed!

No problem! I had to google how to figure out cubic feet since I had no idea when I was asked how much cubic feet I needed!

Thanks again for the cubic feet calculations - I'm already going around the house measuring things!!

But a question - lets say I have a few items of furniture that I would like to take with me, can i still put them on my pallet or (more likely, as I don't think my stuff will fit on a pallet) in my shared container? Or do I have to figure out a way to box them up?

Thanks again for the cubic feet calculations - I'm already going around the house measuring things!!

But a question - lets say I have a few items of furniture that I would like to take with me, can i still put them on my pallet or (more likely, as I don't think my stuff will fit on a pallet) in my shared container? Or do I have to figure out a way to box them up?

I didn't ship any furniture, but the guidelines I was given by UPakWeShip said to take legs off of tables and dismantle other furniture and either wrap them in blankets/bubble wrap or build a box around furniture with cardboard just for the sake of protecting things.