How to choose an edition/translation of the bible?

Is it correct that there are different English translations of the Bible? And different publishers, different editions, or prints?

Yes. Even normal books sometimes have multiple editions. Books which are translated may well have multiple translations, because different people have different opinions on how they should be translated. As one of the most influential collections of literature ("The Bible" is technically a collection of several dozen different manuscripts, an "anthology" if you will), written originally in "dead" languages, and being read over a period of thousands of years by people speaking nearly every language to exist, it's no surprise that there are a great many translations and "editions" available.

The King James Version is one of the best known, and dates back to 1611. Given how much English has changed in the mean time, it's hardly surprising that there have been subsequent translations, and even revisions of KJV. (Some of those other translations have themselves published at least one additional revision.)

Moreover, as a particularly contentious collection of text, accusations of translator bias exist (and are more evident in e.g. the New World Translation).

As an aside, since "the Bible" is actually a collection of (related) documents, and not everyone agrees on what those documents should be, the term "Scripture" will sometimes be used instead.

Is the title of such a book usually "Holy Bible"?

I would say that the name of the translation often serves as the "title", but may be accompanied by "Bible", "Holy Bible", or similar. For some translations, it may not be obvious simply from the cover that a particular volume is "the Bible".

Which of such books are recommended?

The New International Version is something of an old standby... but it is an older translation, and, while it isn't terrible, many sects consider it less than optimal these days. Personally, I would recommend a more modern translation, such as (in lexicographical order):

• The Evangelical Heritage Version
• The English Standard Version
• The New Revised Standard Version

All of these are more-or-less "literal" translations. There are various "paraphrase" translations which may be easier for a new initiate to read, but I would recommend these as introductory at best, as they are likely to lose nuance and be more subject to the translators' theological biases.

I'm also going to disagree with the other answer, and assert that there are a variety of bad, even execrable, translations. As noted, there is a huge motivation for certain individuals or groups to publish a translation that pushes a particular theology. I already noted the NWT, which is deliberately mangled in an attempt to support the theology of Jehovah's Witnesses, who are considered non-Christian by mainstream Christianity.

For more examples, consider these articles and see also How should we judge the trustworthiness of a given Bible translation?. Fortunately, it isn't terribly hard to avoid such translations, as they are infrequently quoted and (except for NWT) rarely endorsed by churches. A translation that is accepted by a wide variety of churches is usually a good sign.

Are they free online and downloadable, or do they need purchase?

Bible Gateway makes the text of a great many translations available online for free. (In fact, I would go so far as to say that a translation not available the TBG is one you probably shouldn't read... although that doesn't mean that every translation at TBG is good.) However, while it's an excellent reference resource, it's probably not ideal for simply reading through Scripture. Specific editions may also have their own websites with free online reading. Electronic copies may need to be purchased, although it will depend on the translation. (KJV, for example, is in the Public Domain and can be obtained from e.g. Project Gutenberg.)

Most translations are available in print, and, while these obviously cost money, if you are truly destitute, you may be able to obtain a free copy by inquiring at a local church, or even from a hotel courtesy of the Gideons.

There are many English translations. Many of them are available online free at Bible Gateway.

What you find on the cover can range from "Holy Bible" to "New International Version" to "Good News for Modern Man" to "The Way." But the usual term is "the Bible."

I am not aware of any translations that are thought to be downright bad. (Be aware that The Living Bible is a paraphrase not a translation; and the Amplified Bible is overstuffed with synonyms -- it's more a study guide.) A newcomer to English shouldn't use the King James Version or the New King James Version as the language is difficult. The New International Version is commonly used by those that want contemporary language, and it's the one I hear the most about other than King James.