Tough to know at this stage as very little has been published. I suspect the first thing we will see will be management restructuring - integrating two (or in TUI's case more!) companies is always a struggle and may take some time. In regards to the charter market, and how it will respond, we are now going to see two key players competing for market share. Perhaps this has all come at the right time with further pending climate change policies likely so how the companies decide their long-term strategies will be interesting. Growth is obviously key so we may see cheaper package deals emerge to allow more consumers to get in on the action, digging at niche markets that have been left to specialist tour operators until now but generally attemts to out price each other.
In regards to the airlines continuing to operate individually or to merge, we still don't know. My personal opinion is that MyTravel will become Thomas Cook Airlines more to do with brand awareness than anything, plus it is not as visible a company as the others (all of whom have high street stores of the same name, ie Thomson Holidays, First Choice Travel etc.). I have no idea about the TUI/ First Choice merger. TUI is rebranding all of its subsidies over the next 18 months or so to all be TUI Airlines, so that means we will no longer be seeing Thomsonfly airlines. With this in mind, perhaps they might choose to get maximum brand exposure and take on First Choice, but First Choice in themselves are a very strong company so they would be benefits in keeping both airlines seperate. We'll see though.
With fleet expansion, recruitment etc, there will be a significant slow down for a while as the new combined assets (both aircraft and people) are assessed and compared with what they require to meet what is set out in their respective stratefies. All of this is just conjecture on my part but I hope it can be of some help.