Options for a teaching position in a liberal arts college in Europe vs US? I am a 4th year PhD student doing Computer Science in an Ivy League School. During the past months the question of what I want to do once I graduate in the next 2 years seems to absorb most of my time during the day. 

I have crossed industry out, and I don't feel particularly strong for a research position in an academic or research institution for various reasons. Instead I realize that I am more intrigued by the teaching process, since I love interacting with students and helping them discover the numerous possibilities that CS has to offer. I would love the idea of following a teaching path in a liberal arts college but I have many concerns that derive from conflicts of interests (in my head). I would love to hear your opinions and advice. 

1)In theory the easiest way to follow would be to apply for teaching positions in liberal arts colleges in the US. My concerns are: I am an international student, that means that they would need to sponsor my visa status. Why would they choose me instead of an American candidate, since they wouldn't have the language barrier and would cost significantly less. More importantly, since the PhD program I am currently enrolled is heavily biased towards research I feel that I cannot demonstrate an impressive teaching portfolio. My teaching experience is limited in a couple of courses I have TAed and seminars on didactics and pedagogics. There might be a possibility of teaching a class on my own before I graduate, but it is a long shot and something that does not happen really easily in my department. If I wanted to follow this path what advice would you give me in order to better prepare myself and become a more competent candidate? 

2)Given that I come from Europe I am more inclined to return closer to home. Every time that I search for teaching opportunities in Europe though I come to understand that it is extremely hard to get in an educational system that I do not speak the language, I do not have the corresponding citizenship, and I am not particularly interested in doing research. The descriptions of the jobs that I am finding are in German, French, etc, and I do not speak any of these languages. Is there even the notion of teaching schools in Europe? How can a holder of a US PhD try to acquire such a position? I am even more lost here since I have no idea where to look for jobs and if there are any that would match the profile of a professor in a liberal arts college in the US.
As ff524's comment suggests, you seem to have a couple different questions, so this is only a partial answesr:

One thing to consider is that, if you have little experience teaching, you may not have an accurate view of how much you will like it as a career.  This is not to say that you're wrong, just that you might want to view teaching jobs not just as a chance to "do what you love" but also as a chance to explore options and find out what you love.

Also, liberal arts jobs and teaching jobs are not synonymous.  At least in the US, there are a number of teaching-focused jobs other than those in liberal arts schools --- notably visiting professorships and jobs at two-year colleges.  As the name suggests, visiting professorships typically last only for a limited time, perhaps a year or two.  However, this could be an advantage if you want to take a shot at a teaching career: you get a chance to teach for a while, and at the end of your time in that job, if you like it, you have more teaching experience can more confidently apply for a permanent teaching job; if you don't like it, no problem, since you're leaving anyway.

Jobs at two-year colleges ("junior colleges" or "community colleges") are also an option.  These jobs are often perceived as less prestigious than jobs at four-year colleges, and pay is often lower.  However, there are a lot more of them than teaching-jobs at four-year colleges, because essentially every community college faculty position is devoted primarily to teaching.  This, again, can make it a good option if you would like to gain teaching experience and see how you like the teaching life.  It will probably be easier to get a teaching job at a community college than at a liberal-arts college.

As Brian Borchers notes in his comment, there are also "regional" colleges that offer four-year degrees but are primarily oriented towards teaching.  These are somewhere in between community colleges and big research schools.  At these schools, research would be part of your job, but not as much as at a major research university.

If you have the chance to teach a course before you graduate, do your best to make it happen.  If that turns out not to be possible, try to get some other kind of teaching experience.  For instance, you could teach a workshop or short class as part of a conference or the like.  As you might expect, it's difficult to get a teaching job without teaching experience, so if you really want to do that, you should make maximum use of your remaining time in grad school to get whatever teaching experience you can.