-I don't suppose there is a real helpful procedure that is also economical?!
You suppose correctly. This is a fairly costly process, and will make you think about what you think you need versus what you actually need. I've made so many trips to Goodwill already.
-Like how do I time everything, how do I deal with the movers (what to expect, what to make clear etc.).
-Will they ship it over and then I tell them when I am in our new home and they will bring it?
There are many companies who will come to your home and box up your belongings for you. Some companies do not. A company like Ranier, which is one of moving scam's endorsed (and more expensive) companies, sends a rep to your home to give you an estimate. And in order for them to give you insurance, they have to have seen what is in the boxes, hence why a lot of them will pack for you.
On your part it will just involve a lot of organization, I imagine. I've started boxing things (but not taping them up) and writing a rough inventory on the side of each box. This will give us a good idea of how much we are going to need to ship. To give you an idea on size, most companies have a minimum of 100 cubic feet. A medium size box is 3 cubic feet, a book box is 1.5, so that gives you an idea of how much you can send.
Depending on the company you choose, they will come pack and pick up your belongings and then in 6-8 weeks deliver them to your doorstep. If you have to change your delivery address for any reason, that's really easy to do. If you want to do it cheaper, some companies (like U Pak We Ship) will allow you to drop it off and pick up yourself. But that doesn't sound like your cuppa.
To answer your other questions, we haven't completely ruled out sending a few boxes by USPS first - especially with the flat rate thing they have going on. But I don't really think this is the most efficient use of my time or money. I would, in your case, just make a visit (or a phone call) to a local Mail Box Store type place that has all sorts of shipping options. They can likely give you an idea of cost for various companies.
And a note about DVDs... you may have already heard this, and I don't want to overstep, however the UK is a different region (2) and also broadcasts in PAL, not NTSC like here. So unless you are bringing a DVD player with you, of which make sure to check the voltage to see if it will work (although it should do with a step down converter) I wouldn't bother with the DVDs. We brought a few PAL DVDs we thought we couldn't live without (we had a portable region free DVD player) when we moved from the UK to US and they've sat in a box ever since. They are actually coming back to the UK with us to go to a charity shop.
I would definitely recommend just research research research! And beware the scams. Just because it is cheaper does not make it better.