If you know me you probably know that you would find few stauncher proponents of free trade than me. Basically if you would ask me if any country should remove a barrier for the movement of any kind of commodity the answer will always be yes. This includes raw materials, products, people and money. If someone said that the US would unilaterally remove all trade barriers tomorrow and allow everybody who wanted to migrate here do so my response would be that it's about time. You still need to keep customs around because stuff that is actually illegal here should still be kept out regardless of if it is baby killing formula, drugs or criminals.
If you read economic theory about free trade it will almost always lead to an increased economy. The beauty of having a growing economy is that even though there are winners there doesn't need to be losers (Since what happens is that instead of someone getting a bigger slice of the pie the pie actually gets bigger). The reason that I do not fear free trade is that I feel comfortable that I myself don't really have a problem to compete with anybody doing what I do no matter where in the world they live. If I was working in a job where little training was needed like for instance in a call center or flipping burgers at McDonald's I should probably be worried because there is most likely going to be someone around from a lower wage country that would do it cheaper than you want to.
Usually what happens when you open up trade is that you get to specialize on what you are good at. So basically if you are a country that keep people well educated that means that instead of having a bunch of people working low level tech support or the aforementioned call centers they can be senior tech support or managers. The jobs requiring little training will still need to be done but instead of wasting your countries labor force on that you can have others handle that for you and you instead can export the know how of higher level jobs. The country providing the "low wage" work force will also gain from this because they will be able to take advantage of know how not available to them domestically.
Here is where education comes in. Even though both countries involved above gain you probably want to be the one providing the high level services. The way to become that one is to make sure that you have a well educated population. How do you get that? You make sure that nobody is denied going as far as they can in the education system regardless of their economic situation. This is definitely not the case here in the US. Even though there are a lot of scholarships and stuff available a college education is not something that is available to anybody who could pass it.
I'm not saying that we should keep everybody in school until after college. You still need to keep entrance standards and make sure that you don't let too many people in that will probably not graduate. All I'm saying is that we should let everybody who could pass college do it regardless of if they have the economic means to do it or not. Even if this means that we as a society have to pay for this in the short term it is something that will be paid back many times over counting over the life time of the person even if you just count the increased income that the extra education will generate (Higher pay will lead to higher taxes).
One thing you need to be careful about though is to not make it too cheap. Taking Sweden as an example where education is basically free all the up through post grad (You also get a monthly stipend to live on). The problem with that is that I know a bunch of people who just go to school because they don't have anything better to do (Or they don't feel like working). You should need to pay at least a little so you make sure that there is at least a little bit of thought going into the choice of education as a way of gaining an occupation instead of just personal growth. One example would be to make the college free, but not providing the stipend. This would still make college something that takes a little bit of investment, but it probably would not be out of reach of someone who really wanted it.
Higher education means that everybody are better suited in an increasingly global society (It's coming regardless of if we want it or not). Also over the long term this will make us money because people will get increased wages (And keep in mind that you would no longer need to save for your children s college fund anymore or at least nowhere near as much). There are also other savings coming from the fact well educated people with good paying jobs are probably less likely become criminals, end up on well fare or otherwise end up being a burden on society. And finally there is also the individual gain of people with high education usually having more oportunities available to them and hopefully being able to lead more rewarding lives.