As you have gathered, online certificates are not really worth the paper they are written on. They do, however, offer a reasonably cheap insight into what TEFL involves. I did one as a sort of 'taster' course and the knowledge I gained from it gave me an edge over my fellow trainees when it came to doing the CELTA.
In terms of further training I'd strongly recommend that you look into doing a CELTA or Trinity CertTESOL. Taken intensively over four or five weeks, both are 120hr in-person courses which include the all-important 6hrs of observed teaching practice (teaching real students). At £1,000+ they don't come cheap but will open more doors from day one than an online TEFL certificate and a "weekend" course ever will.
Talking of which, steer clear of "weekend" TEFL courses. An increasing number of employers refuse to accept them as the "teaching practice" involves teaching fellow trainees rather than real students.
That said, before you look into further training, you need to consider where you want to work. You may not be aware that the options for those without a degree are seriously limited and that the list of countries where you can legally work is rapidly decreasing. Currently your best (confirmed) bets in Asia are China, although a degree is fast becoming a requirement to get a Z Visa, Cambodia and Laos. Note that by 2015 with ASEAN integration (the Asian EU) neither Cambodia nor Laos will be an option.
In South America, Costa Rica and Ecuador still accept those without degrees. It may be possible to work elsewhere in South America but I don't know for sure. Rule no. 1 of TEFL: do your research! :)
As you hold a passport from an EU member state, the whole of Europe is open to you. However, countries such as Spain, Italy and France are very popular with TEFLers so I'd recommend getting a CELTA or Trinity CertTESOL to give yourself the best chance of finding work. Note that no matter where you teach, some schools will insist on your having a degree.
Finally, you mentioned internships. Personally I think these are great for gap-year types who may not have travelled abroad and who want some guaranteed (paid for!) in-country support. However, I wouldn't recommend them for would-be career teachers. I've come across a few organisations who offer internships. Closer inspection shows that they place teachers in Callan schools (a fairly laughable method of "teaching" where teachers are basically script readers) or schools where you are merely a native English-speaking novelty - local teachers plan the lessons and teach the students grammar and vocabulary. You meanwhile get to talk to the students under the watchful eye of the local teacher. Doesn't sound like teaching to me!
Ooops! I seem to have written an essay! I hope it answers some of your questions. Feel free to ask any more.