Know-How Exchange : E-Marketing

You'd probably find a sensibly formed search + display network campaign the kingpin of all your online (and offline) activities. It's fast in giving real responses to real questions - and any argument between two elements can be adjudicated simply by split testing and letting the purchasers give them the answer.

This information can be reverse-engineered into SEO activities (which by comparison to search campaigns is slothful) - and the better leads can be captured using email lists that go on to explain the nature of the company in better terms. This is then part of the social side of your marketing rather than just the rounding up of leads. Knowing what your customers like means you can use all the media you mentioned in a far more effective (= targeted) manner.

Once you've gotten this far is the time you can send it back into the world of printed media, direct mail et al - knowing your ads will have maximum effect.

Your main problem is that a budget airline usually doesn't have much in the way of specialness. All the best campaigns have some form of USP. Sadly hammering price has led to people beggaring themselves to get work when they should have looked more carefully at their business activities. After all, an airline like Cathay Pacific will make 75% of its profits from its first class passengers - who cost the airline only a little more in terms of expenditure. Their tourist class seats just keep the plane in the air - and this is all a budget airline has by way of generating profits. It's a tight corner to be stuck in, and one that they have painted themselves into.

PS I'd flown 100,000 miles by the time I was 12.

Does the airline serve unusual airports? If so, target your audience based on this.
Pay-per-click is likely to be a good choice for online as well.

What you listed ("Facebook, Linkedin, You Tube, Twitter, Instagram") is more known as social media, which is part of online. But in general, online also brings in all sorts of places where advertisement can be run. Search ads (Google, etc.), media web sites (magazines, etc.), blogs, etc.

My first thought would be to look at travel web sites and sites related to cities the airline flies to as places to consider placing ad in.

Corporate level online advertising usually refers to the big display networks and professional media (eg mainstream newspapers, tv channels etc) including adverts that go beyond simple banners and text ads (though it will include these too). There are specialists in this area - from creative work - eg how a campaign works across media and links in to landing pages, microsites etc - to media buying operations. If the budget is potentially large and you're not familiar with a sector it might be worth looking for partners or external consultants with a track record of larger online campaigns.