This guide is for those who enjoy playing Final Fantasy XIV, but don't have too much time to put into it, want to play what they want to play in the game and not what the game thinks you should play, and spend more time playing other games, or with their partner, family, practicing kendo, eating out etc etc. Yes, you. No, not you, her next to you.
This guide will begin with the simple things you probably already know and get to the real advice at the end.

UP TO LEVEL 60 / ILVL 145
There are many guides already available, but you should use this time to read up on your job and practice the skills as you acquire them. Make sure to unlock and try all the content you can at your own pace, take your time, listen to help given by others, don't let the people with anger issues get you down, and hopefully by the end you should mostly have enough Level 58 gear and a piece of Law to get you to iLvl 145. Ignore Coil and the Extreme primal fights for now though, you can come to those later. This will probably give you two to three months of great content at a gentle pace.

LEVEL 60 / ILVL 145 to 170
Welcome to the endgame, because by now you've cleared all the story content and now you can spend your time repeating what you enjoyed and getting your playing ability up to the level needed for the harder challenged. Remember that at Level 60 how you play your job is radically different from 1-59 in many cases, so read the guides, practice against dummies to start and then use the other content to perfect.
The next stage to unlock more content is iLvl 170. This is really quick and easy to reach. You will need to buy equipment using Tomestones of Law from Hismena in Idyllshire(5,5). Tomestones of Law drop from all roulettes in plentiful supply, as well as hunts and pretty much everything else you can do. The best roulettes to run are the Expert and Level 60 ones, which you can also run with friends, as they drop Esoterics too, and are the slightly more tricky dungeons in order to practice your hand at while you're still learning your Level 60 rotation and abilities.

LEVEL 60 / ILVL 170 to ILVL 200 and beyond
So, now you have a full set of iLvl 170 (almost). You will need one extra item to offset the single iLvl 160 ring you probably still have, which you can buy with Esoterics. You should ideally be saving your Esoterics for the iLvl 200 weapon, as this is the only thing I'm going to recommend buying with them, but if you're in a hurry you could buy a iLvl 200 ring first which will get you over 170 which is required to enter Alexander (normal).
Once you have iLvl 170 then you can enter Alexander (normal). This is an incredibly efficient way of going from iLvl 170 to iLvl 190, and you can now run it as many times as you like.
Once you have iLvl 175 you can enter the 24-man raid Void Ark and at iLvl 179 you can enter exploratory missions. The Void Ark can provide one piece of iLvl 200 (Esoteric level) armour per week (no weapons or accessories) in one drop, if you're lucky enough. Exploratory missions have promise too but we don't know much about it yet.
Use any spare Esoterics you get after your weapon for accessories, as you have no other sources of iLvl 200 accessories. After you have full iLvl 200 weapon and accessories, use any remaining for that final piece of iLvl 200 armour/clothing that annoyingly just won't drop from Void Ark.
Congratulations, you're now iLvl 200 without too much grind.

THE TICK AND THE TOCK
Now are the key points about what you can do and what you should do. Before we proceed you need to understand how the game patches work. In reality the game works in six month cycles, each six month cycle consists of two major content patches, one at the start (the tick) and one after three months, half way through (the tock). At the start of the six month cycle they introduce gear at 20 iLevels higher than it was previously, making much of the previous redundant. In short, if your main focus is gearing up, your efforts will be largely reset every six months. Understand this to avoid future frustration.
At every tick and tock Square makes equipment at a level that was available three or six months previously quick to get, and introduces new equipment that again takes a very long time to get. Get the former, avoid the latter.
I have highlighted in bold the tasks that are time efficient and you should do at each stage and in italic those you should avoid. You should get enough stronger level tomestones (Esoterics) for the weapon, even though esoterics are in italic, but it won't take long for just this one item and will get you good practice at the latest dungeons without going overboard.

The tick (last tick was Heavensward launch)
iLvl 170/180 equipment is easy to get (Law tomestones)
iLvl 190 equipment is easy to get but only one a week (Alexander normal)
iLvl 200 equipment requires timesink (Esoteric tomestones)
iLvl 210 equipment requires clearing of very hard content inaccessible without some iLvl 200 equipment and a lot of time, effort and skill (Alexander savage)
The next tick in Feb 2016
iLvl of top gear goes up by 20-30 iLevels
weaker Tomestones (Law) are made redundant, stronger Tomestones (Esoterics) take the place of law, and a new stronger Tomestone takes that place
new super hard content introduced (Alexander savage phase 2)
weaker version of super hard content introduced (Alexander normal phase 2)

The tock (last tock was today, 10th Nov 2015)
iLvl 190 equipment is easy to get without limit (Alexander normal)
new iLvl 200 equipment is easy to get but only one a week for the first month or two (Void Ark)
iLvl 210 upgrade for any Esoteric equipment that you have is much easier to get (although not the Esoterics themselves)
The next tock is in May 2016
new casual 24-man content is introduced
upgrades to the stronger tomestones (whatever the replacement for Esoterics is) become reasonable to get

THE TIMESINKS
There are two timesinks that SquareEnix have devised with one purpose in mind: to ensure dedicated players keep playing and don't stop subscribing. These are incredibly repetitive and should be avoided as much as possible.

The tomestone hole
There are two categories of Lv.60 Tomestones, one that buys you weaker equipment that is easier to obtain, and one that buys you stronger equipment that are available in much fewer numbers. At the time of writing the weaker is Tomestones of Law and the stronger are Tomestones of Esoterics. At the start of the tick the stronger becomes the weaker and a new stronger is introduced. So, at the time of writing, in February 2016 they will make Tomestones of Esoterics much easier to obtain and introduce a new, stronger Tomestone at either iLvl 220 or iLvl 230 to replace Esoterics. So the timesink begins again.
The most efficient way of getting the stronger Tomestone is by repeatedly running the Expert roulette once every night, which consists of only two dungeons. In short, the easiest way to get the best gear is to repeat the same two dungeons every single night for a very, very long time. This is clearly not the most enjoyable use of your time when Witcher 3 is sitting there waiting to be played. You do not need to do this to get the most out of this game and access any content (see later), and I would recommend that you only get enough of the stronger Tomestones to get the new weapon, and then use any spares you get later for accessories (starting with the ring) as it's the only easily accessible way to get iLvl 200/210 weapons and accessories.
You should get your iLvl 200 (Esoteric strength) armour/clothing from the 24 man raid instead, where each piece only needs to drop once, although there is a random factor here instead. The only disadvantage is that you can't upgrade it to 210 later like you can with Tomestone gear, but 10 iLvl is nothing for most content and just wait another few months and it won't matter anymore.

The relic weapon questline
If you think that the method of getting Esoterics sounded a joyless slog, then the relic questlines will make them seem a bed of roses. The relic weapon questline produces a weapon of the highest quality, providing you're willing to complete the insane list of banal tasks required to get it, many of which have incredibly low success rates based on random drops, merely designed to chew up your time.
I would ignore it completely unless it's later revealed that they've made it much shorter, or if you actually enjoy the tasks that are required to get it. Buying a weapon with tomestones is much easier and usually only about 10 iLvls below whatever the relic weapon is at.
It's a shame, because the original questline until iLvl 90 was really good.

COMPLETING HARD CONTENT
Having three month old gear will not in any way stop you from completing any content without much difficulty, except for the latest hardest mode content.
There is content such as Coil, Alexander (Savage) and Extreme primals that you cannot clear without time, effort, and the latest gear when it first comes out. If you're not willing to farm Esoterics then for the most part these are closed off to you at launch. If you wait three or six months you will be at an appropriate level to do them and Square will have introduced echo to make it easier. So, at iLvl 145 you can do all the non-Heavensward hard content (eg. Coil) and at iLvl 200 you can do absolutely everything at the time of writing, including the latest extreme primal in 3.1.
Because you are avoiding the time requirements to get the highest level gear the moment it is available doesn't mean you are blocked off from doing any content. You will just need to wait a little. You could try finding other like minded people to start a static for those with little time (maybe just one night a week, for example) and see how far you get.