Most languages have fairly strict syntactic rules for the relative placement of words, but Greek has very few of these. One reason is that the affixes on the words show which words go together to form a unit, being it a phrase or clause. So, for Greek the word order is primarily based on semantic and pragmatic considerations. The basic rule is that the more to the left a word occurs within its scope (phrase or clause) the greater is its prominence compared to the other words in its scope. Some words have an inherent semantic prominence (words like all, and the demonstratives), so these are placed before what they modify, unless something else is more prominent in a particular context. When a demonstrative is used to contrast two items it comes further to the left than when it is used as a back reference to something already known.
I wrote a brief introduction to word order in Greek in the paper “Word order and relative prominence in New Testament Greek.” It can be found among other papers here: http://sil.academia.edu/IverLarsen/Papers
The main clause in 1 Tim 4:6 is: καλὸς ἔσῃ διάκονος Χριστοῦ Ἰησοῦ.
The word “praiseworthy/good” comes before the noun it modifies because there is a contrast between a good and implicit bad servant. A good
servant is one who teaches τοῖς λόγοις … τῆς καλῆς διδασκαλίας – the words of the good
For the verb εἰμί it depends partly on semantics, i.e. does the verb indicate existence or does it only function to describe or identify an entity. The more semantic weight a word carries the more to the left it occurs. The other aspect is the relative prominence of the verb compared to the other elements.
If ἔσῃ had been placed last, the meaning would have been: ”you will be a good
servant of Anointed Jesus.” However, when it is placed in the more prominent position as here, the meaning changes slightly to: “then you will really/truly be a good
servant of Anointed Jesus.” English indicates prominence mainly by stress but also by adverbs and to a much lesser extent by word order. Greek prominence is usually lost in traditional translations of the Bible, which is an incentive to study this crucial topic. It is complex but in my view simpler than Dik and Levinsohn make it out to be. It is governed by principles rather than fixed rules that can be put in a formula.
You may want to look at other places, e.g.
Mark 12:28 Ποία ἐστὶν ἐντολὴ πρώτη πάντων; - Which commandment is really first of all? It was a common discussion topic among rabbis which commandment was the most important. So, what Is Jesus’ take on this discussion? Which do you say is really the most important? If ἐστὶν had been placed last, the meaning would be: Which commandment is first of all? As if the person is simply asking for information about what he does not know rather than wanting an opinion on a controversial topic.
Matt 21:10 Τίς ἐστιν οὗτος; - Who is
this man? The order Τίς οὗτος ἐστιν; would give a slightly different meaning: Who is this man?
Mark 4:41: Τίς ἄρα οὗτός ἐστιν...; Who then is this man
Mark 1:27 Τί ἐστιν τοῦτο – What is
Matt 22:20 Τίνος ἡ εἰκὼν αὕτη καὶ ἡ ἐπιγραφή; Of whom is this picture and writing? Notice that αὕτη comes after its noun, because there is no contrast between this picture and another picture. It is simply a reference to an entity in the environment (which linguists call deixis). It could have been repeated at the end, but Greek prefers ellipsis in such cases. There is no ἐστιν in the sentence. It is pushed so far to the right that it is pushed over the edge and do not appear, since it is not needed. It carries no semantic weight. Notice also that question words come first because theya re inherently prominent, and normally has stress in English.