Congratulations on your new posting :-D ... I can't comment on the cheapest way from your area as I live in a different country. I can comment on international cargo shippers in general from Aus > Canada and perhaps they may service your country, at this stage I have 6 separate companies I have lined up to provide me quotes...but that will have to come later once the lil ones are in bed as to their names....
As for the contents front, we are in the same predicament however with a bunch of little ones also (not sure if you have any kids/young/older/will be coming with you tho).
Through my research I am finding that what we have 'approved' safety wise (car seats/cots for the kids) in Australia are not approved for use in Canada - don't know if any of your stuff falls within that category (we are selling/giving away "safety approved" items in Aus specific to Australia as there is no point bringing it to Canada when it's not approved!)
Whilst we are sourcing a 40ft cargo container.... it's still hard to 'get rid' of your loved belongings.... (my husband nor I am willing/wanting him to part with his FJ40 just as I am not willing to part with some of my antiques - the marital trade off - hahahah!)
however.... the way I have tackled this issue for us is I've made a list and have divided them into the following categories:
1. A given - will come regardless
2. Nice to have (rated 1 to 5 being the highest ranking of 'nicest to have' and so forth)
3. Don't need
If I can get some extra space then those listed within the top of the 'nice to have' rating and preference based would get the space on the cargo container.
May seem a little anal, but hey....
It's always going to be a hard decision as to what comes and what goes. If you have plans on coming back to your home or have an investment property perhaps see if family would be willing to 'look after' some of the items or you can house them within your investment property (such as a rental)....
Allot of what we have child related will be given away to our family and/or donated to those 'less fortunate' than us.... and the rest perhaps in the rental or sold towards 'funding' our journey :-D.....
Also, as a suggestion perhaps google "downsizing, what to choose", or, some other search engine string of words.....??
It's so hard making the decision, but perhaps an even easier option - look at the day to day stuff that you use inside and outside the home... even if it comes down to what pillowcases and teacups you use the most and if you have a property lined up, look at the space inside of your new property and see what will fit and what you will use in and out :-D....
Good luck with it - no idea if I have been of any help... (I know we'll need it sorting stuff out lol) :-D
Cheers,
Lolla