Do your best

'Beautiful' is clearly more than one syllable, so it does not form a short comparative; the superlative of 'well (-) kept' (or indeed 'well- [anything]') is 'best-kept', as you might have heard or realised (e.g. 'the best-kept secret in the City'). This does not mean the best village, or the best secret, but the one that is 'kept' to best advantage (in whatever sense of that term: holding a secret without betraying it to anyone; maintaining a village in good decorative order).
There was, and/or still is, a national competition scheme for Best Kept Village at county, regional and national level in Britain.

Answer 1 entails a different metaphor for 'mental acuity': sharpness ( = ability to penetrate straight to the 'core' of an argument ) rather than 'brightness'.
Answer 2 follows the shape of the phrase but is simply a made-up example; Answer 3 is sometimes heard, but it is rather a tired phrase now (a clichE, indeed) and in any case contains no superlative. Answer 4 is a mis-combination of 'thick' (a widespread traditional expression of stupidity, typically as in 'thick as two short planks') with 'the best idea since sliced bread', i.e. approval of some smart, convenient new invention (however trivial).

Answer 4 is the only one offered which does not incorporate a superlative.

Only Answer 4 offers a true superlative; we don't usually make the 1-word ' ~-est' form except with single-syllable adjectives, except perhaps for satirical or childish effect ('Think of the beastliest trick you could play on your neighbour').
We nonetheless hope you would never have cause to wish to say anything of quite this kind during your time in Britain.

While Answers 3 & 4 are vaguely possible here, but rather 'wordier' than necessary, the alliteration of 'first and foremost' (Answer 1) adds extra pungency to its actual meaning.
The phrase in Answer 1 is a great favourite among advertisers ('You'll find our service/product is second to none!') but does not quite fit here ~ because although Lear was indeed generally regarded as the pioneer of the Limerick, others writing after him have produced plenty of technically better examples; so, taking the corpus of all such poems as it stands, Lear is not the overall absolute master, and this phrase is therefore not appropriate. (He often just returned to an echo of the first, defining line of a Limerick at the end, instead of providing a third rhyme and a punchline that clinched the little story.)
You may well wish to explore the Limerick yourself in a class, conversation or friendship group, or indeed online, as a concise and classic sub-genre of English language and culture. Please be warned that there is a robust tradition of Limericks which are critical of certain people and groups (possibly such as yourself) ~ way beyond the boundaries of Political Correctness ~ but which some people still find clever and/or funny; and that there are plenty of obscene examples (you may be able to hear the 'four-letter words' waiting to drop into place at the end of such a story ... and only if you're that way minded, it can be an informative way to explore English slang and vulgarisms. You Have Been Warned though ~ and you would need to be very sure indeed of your company before reciting any examples unless you are quite sure they're 'clean'!)

Most of these are good pairs within their contexts, but Answer 1 is strongest since the superlatives are still expressed in 'linear' terms of the front-running and hindmost portions of the train.
'Head and tail' is a good pair but for some reason is not really used to refer to vehicles, except in the specific context of 'head and tail lights (or lamps)' on road vehicles ~ or possibly trains.
'First and final' (despite an attractive alliteration again) is more often used about something which is simultaneously the 'one and only', e.g. that someone who has seriously misbehaved (at work, or on a sports field, perhaps) is given a First and Final Warning not to repeat their misconduct, else they would face outright dismissal on any second occurrence. We believe that modern Contract Law may well prohibit such drastic treatment except in the most compelling of circumstances (e.g. a doctor or teacher who 'couldn't keep his hands to himself'), but we are confident you will appreciate the sense ~ at least, linguistically! ~ of such a phrase, and that it does not apply readily to trains.

'Topmost' (Answer 3) works well here; 'highest' (Answer 1) might be taken to mean those that measured the greatest from bottom to top of their glass, rather than those situated furthest up the doomed building.
Answer 2 is not a normal proper superlative, though it does crop up in the stylised diction of some typical Church chants which refer to God as 'the Most High'.

Answer 4 is not wrong, but the word has connotations of something being necessarily of inferior quality (as in 'cheap and nasty'). Answer 1 is a false attempt at a negative comparative; Answer 2 is wrong because the correct formation from this monosyllabic adjective is already offered at Answer 4.
The true answer may sound like rather a wide and plummy paraphrase, but in the likely words of an industrial salesman (which appears to be the case in context), it is almost certainly what he would say.

Answer 1 may seem perverse with its apparent double superlative, but the meaning is strong and poignant in these tricky circumstances: there may be several other choices, but this one will potentially cause less further pain and damage than any of the others.
Answer 2, and certainly Answer 3, feel inappropriately glib, while No.4 contains a mis-formation of a superlative from a non-monosyllabic adjective.

Answer 4 is much the strongest, with adverbial elements both of time ('throughout') and figurative space ('at the forefront').
Answers 1 & 2 are perfectly possible, but noticeably milder in their expression and effect.