What are some methods I can use to look for and find an Ancient Greek Bible that I can buy and use? My goal is to find one that would be as accurate as possible to the manuscripts. If my use of "manuscripts" is vague (b/c not all manuscripts were EXACTLY the same) or represents a naiveté of the subject, please correct me. And if so, perhaps this next question can be answered: Is there a version of an Ancient Greek Bible that is generally held to be the most reliable? That would probably be the one I want to get my hands on.
The Nestle-Aland/UBS text is standard. This is an edited text which shows what the editors think the original text was most likely to be based on the evidence they have researched. The NA and UBS names refer to two editions of the same base text. They have occasional differences in punctuation or spelling, but the main difference is their apparatus. The main body of the text shows what the editors think is the most reliable option for each verse, but it then has detailed footnotes showing the evidence for all the textual variants, as well as a confidence rating. The apparatus shows not just which families of texts have which variants, but even lists the individual manuscripts for hundreds of the earliest known manuscripts. Even if you disagree with the editors' choices, the apparatus is an invaluable tool, letting you see the evidence to make up your own mind. The biggest difference between the NA and UBS editions is their apparatus: the NA apparatus is somewhat more detailed, while the UBS apparatus has some material that is useful for translators. Copies of the UBS5 text are $31USD with free shipping worldwide at the Book Depository. (The description is in German, but this is the same ISBN as those sold in Australia so I'm pretty sure it's got English footnotes.)
Or if you're happy with a digital text then the SBL GNT is free. It is a different edited text that mostly agrees with the Nestle-Aland/UBS text, but disagrees in 540 places (out of possibly as many as half a million total textual variants). Its main draw back is its inferior apparatus, which lists other edited texts rather than their sources. But hey, it's free!
The Tyndale GNT is another new option, but I don't have any personal experience with it yet.
The Englishman's Greek New Testament, available widely, has the Stephens Text of 1550 and an interlinear, literal, English translation. It is one of a few almost identical Greek texts which are commonly called the Received Text or the Textus Receptus.
This is the Greek text behind the Authorised Version (the King James Version) and is the Greek text used by Martin Luther and by William Tyndale.
This is the Greek Text that stood for over four hundred years from the times of Erasmus, through Stephens (1550), Beza (1598), Elzevir (1624) and Scrivener (1894) there being very little difference between these five texts across four centuries.
The alternative, the Westcott & Hort and the Nestle-Aland texts rely heavily on the Codex Vaticanus and the Codex Sinaiticus - both introduced in the middle 1800s.
One has to make a decision whether one accepts that these two ancient manuscripts survived because they were little used (and therefore were of doubtful veracity) or whether one accepts that Divine Providence kept the most important codices hidden away for almost two thousand years from their being used by the followers of the Lord Jesus Christ.