You have no control over which airline you are booked on, so each trip could potentially be on a different airline.

No single frequent flyer programme will give you miles regardless of the airline you travel on.

First, a little background that will hopefully explain the best way for you to choose which, of multiple, possible frequent flyer programmes to join:

A large number of the best-known airlines around the world have grouped themselves together in on of three big so-called "alliances" - Star Alliance, oneworld, and Skyteam. Most of the well-known airlines you have ever heard of are likely to be a member of one of these alliances (the obvious exceptions are Emirates, Etihad, and one of the airlines you mentioned - Jet Airways).

An airline can only be in one of these alliances.

Star Alliance includes the likes of Lufthansa (and their related European airlines, such as Austrian, Swiss, Brussels Airlines, LOT, etc), Singapore Airlines, United Airlines, Air Canada, Air China, Asiana, ANA, Thai, etc. See http://www.staralliance.com/en/member-airlines

oneworld includes the likes of American Airlines, British Airways, Cathay Pacific, Malaysia Airlines, Qatar Airways, Qantas, Iberia, Japan Airlines etc. See https://www.oneworld.com/member-airlines/overview

Skyteam includes the likes of Delta, Air France-KLM, Alitalia, Vietnam Airlines, Garuda Indonesia, Korean Air, and many Chinese carriers - China Southern, China Eastern, Xiamen Air - as well as the Taiwanese carrier China Airlines. See https://www.skyteam.com/en/about/

In general, if you fly on a member of one of these alliances, you can earn miles in any programme run by any other member-airline of that same alliance. So, in the Star Alliance example, if you fly Air China you may earn miles with Lufthansa's programme; in the oneworld example, if you fly American Airlines you may earn miles in Qantas' programme; in the Skyteam example, if you fly KLM you may earn miles in Delta's programme, etc.

Each individual airline may have additional partnerships with airlines outside of their own alliance, which may allow you to earn miles on some flights on these other airlines. For example, Air France and KLM will allow you to earn miles on some Etihad airways flights, but with very stringent restrictions.

(Always, mileage earning is never a given. Each individual programme has its own rules and some tickets will not earn, depending on which booking class you end up travelling in...it can be a bit opaque to a beginner, but if you stick around, you will start to get a feel for it).

So, in short, you should consider perhaps joining ONE programme associated with each of the three main alliances - that way, whenever you end up flying on a Star Alliance member flight, you may be able to earn miles in whichever Star Alliance member airline's programme you joined; ditto for oneworld and for Skyteam.

Some other things to consider:

Emirates is NOT in any of the alliances; however, they have a deep relationship - just renewed for another 5 years but no guarantee it will last indefinitely - with Qantas. Therefore, if you were to choose Qantas as your oneworld member frequent flyer programme, you could also earn miles when flying Emirates in that programme.

Etihad is not a member of an alliance (though perhaps that may change in the future). They have a number of partnerships with the likes of Alitalia (in Skyteam, but probably not for long, as Alitalia is in the process of being sold) so, at least right now, having Alitalia as your Skyteam programme would also allow you to place your Etihad flights in that programme.

Jet Airways, that you mentioned, is not in any of the main alliances, but it has a relationship with both Delta and Air France-KLM, such that flying on Jet Airways should allow you to collect miles in either Delta or Air France-KLM's frequent flyer programmes. (Jet and Etihad also have a partnership - for now - so you can earn miles in either's programme, too, when flying on either airline).

If you tend to travel a lot on a particular airline, then you should consider joining that airline's frequent flyer programme. You should then use that frequent flyer programme number every time you interact with that airline - when you check in, when you had over your luggage, etc. Become familiar with their "partners" - have a look at their website and see which airlines they allow you to earn miles on - and remember to quote your frequent flyer number to all those airlines at every interaction, too.

There is little point in joining more than one frequent flyer programme per alliance. So, for example, if you decide to join Singapore Airline's frequent flyer programme, there is little point in also joining Lufthansa's programme, or United's programme, or Air China's programme - because they are all members of the same alliance, and therefore they tend to have the same group of partners, more or less.

Note also that, as you are travelling on what are usually discounted tickets with a greater degree of flexibility than "normal" tourist or business tickets, "normal" mileage earning may not always apply, meaning that you get fewer, or no, miles for some of these types of flights.

You should ask around your colleagues to see if they have any experience or insight they can share about mileage earning on their travels - there is likely someone you know who has this down to a fine art, and you should pick their brains.