My aim for this answer is to be applicable to ALL Christian denominations and theologies on offer today, so it can be a starting point for you to choose. I also aim for objectivity by limiting myself to an overview and non translation-specific features.
Is it correct that there are different English translations of the Bible?
Yes. This Wikipedia section lists all major modern English translations grouped by their
- root: KJV (1611) and derivatives, English Revised Version (1881) and derivatives, NIV and derivatives, etc.
- translation philosophy: many dynamic translations are new projects in the 20th century.
- denominational interest: Catholic (include deuterocanonical books), Jehovah Witness, Latter Day Saints, Messianic / Jewish
- source text: Nestle-Aland (majority of modern translations), Textus Receptus (KJV and derivatives), Septuagint, or strict Masoretic (including the one used in Judaism, published by JPS)
And different publishers, different editions, or prints?
Each translation is done by a group of scholars. Their work is then printed as a regular book by various publishers who also manage the copyright. Usually a translation is published by a single publisher (such as Crossway for ESV, Holman for CSB, Zondervan for NIV, and Tyndale for NLT).
Each publisher usually provides various packaging or bindings options suitable for the reader, some options purely for the "look and feel": some have bigger letters, some have very nice (and expensive) leather bindings, some use cheap paperback binding for inexpensive distribution for evangelism, some use thicker paper for journaling, covers have various color / decoration / material, etc.
Many publishers also offer various study editions by combining the text with various study features: notes, maps, mini dictionary & concordance, indexes, pictures & illustrations, etc.
If there is an update to the translation, there can be multiple editions / printings and the copyright page / preface indicates this; for example, the NLT has gone to at least 3-4 updates (1996, 2004, 2007, 2013, 2015), so it's important to notice which year printing it is.
When shopping, you start by choosing a translation, then select the features you want available for the translation. Online distributors in the USA such as Lifeway and Christian Book Distributors have lots of filters to help you choose the right features you need. Each popular translation can easily give you dozens of options. For denomination-specific editions or Bibles packaged with specialized commentaries, you may need to go to a specific publisher's website such as Ignatius Press for Catholic Bibles or Deseret Book for LDS Bibles.
Is the title of such a book usually "Holy Bible"?
Yes, usually that is the title, to indicate that the original text is inspired by God (who is Holy). Although if it is bundled with notes, the adjective "Holy" can be substituted with "Study" such as "ESV Youth Bible", ""ESV Study Bible", "Children's Bible", "Timeline Bible", etc.
Which of such books are recommended?
I cannot make a recommendation for you since it is highly dependent on your purpose, your preferred denomination, the English reading level, and other features you want (binding, notes, text-size, etc.). If you want a Bible with study notes, then it is very important to know which theology the note provider holds. Even a particular translation that is not sponsored by a denomination (such as ESV, CSB, NLT, or NIV) may have a very slight bias toward a particular theology beyond the translation philosophy they use (literal vs. dynamic).
Personally, I like using NLT (a very dynamic translation) as the easiest to get the initial sense of the text (especially Paul's letters) and use a couple more literal translations (CSB, NIV, ESV, etc.) when I need to dig deeper, along with Greek / Hebrew interlinear if it is important to notice the underlying original-language words in the source text.
Are they free online and downloadable, or do they need purchase?
Most publishers do not allow the whole Bible translation text to be downloaded (unless they are already out of copyright) even though the whole text is available for online browsing through websites such as BibleGateway or Bible Hub (who I'm sure have a licensing agreement with the publishers). If you use a Bible study software such as Logos or OliveTree you can download the entire text for offline use, but you need to use their software to read it.
Most common translation / editions do not require a purchase if accessed via the method described above, but you usually have to purchase a license from your Bible software for these less common editions since they do the work to reformat the Bible text to work well with their software. Unless it is a specialized scholarly editions (with critical apparatus), the cost is usually minimal. Logos free edition, for example, provides 27 English translations for free (including major ones such as ASV, CSB, Douay-Rheims, ESV, KJV, NET, NASB, NIV, NKJV, NLT, NRSV, etc.) which you can download for offline use to be read with their smartphone app.
These are resources that can help one choose a Bible edition / translation: