Do you want to enjoy your holiday and the sights you see on it?
OR
Do you want to waste half your time, NOT seeing much, but the back of a camera, while you prod buttons looking for obscure menu settings trying to work out how to use it?
If you are sure you want to step up to a new camera system, then go for it. Pick the one that is easiest to handle and work. Then spend a month or three going out every evening round your own home, taking photo's of anything and everything that doesn't really matter if it comes out over or under exposed, out of focus or blurred to bluggery, until handling the camera and getting shots the way you want them becomes second nature and you don't even have to 'think' very much to do it, let alone prod buttons and hunt menu's worse, pull the user manual out your pocket and read up how to make it do what you want it to.
As to the choice of kit? I'm not surprised the chap in the shop recommended the 18-300.. that's a £500 lens! bet he was rubbing his hands with glee looking forward to his next commission cheque!
Yup, it covers the range of focal lengths I have in my bag, afforded by the £70 18-55 'kit' lens, and the £180 55-300.. for half the price... and of what I actually use with any regularity, the £180 18-140, would cover all my most used focal lengths even more cheaply.. in fact, the kit 18-55 on it's own almost does, even more cheaply!
Do you REALLY need that much 'zoom'? Ever! Let alone on holiday?
Back in 1980, my father was emigrating to Canada, and bought me an Olympus XA2 compact camera for my 10th Birthday, so I could get 'nice' photos of all I was likely to see when I went to visit him. Then, most cameras had a fixed, usually wide angle lens. Interchangeable lens 'system' cameras tended to be very expensive, and zooms were only really practical on SLR system cameras where you could see through the view-finder how the zoom changed the framing, and even then, they were often shunned, especially for 'travel' photography where you will mostly want a wide or normal angle lens for Landscapes, architecture and people shots... OK if you are going on Safari and don't want to get too close to the lions, something longer may be useful, but in that scenario, the extended reach of a long zoom probably still wont be enough and you'd be better ditching the compromises of a 'do it all lens' for a specialist one for that job.. or forget the camera all together.. enjoy the holiday, and buy a 10p post-card at the souvenir shop, taken by a pro with the specialist kit and the time to wait for the best light and setting and pose!
So, for the most part, that fixed wide angle lens compact has been my favourite 'travel' camera for thirty odd years, and STILL gets slipped into my pocket when I'm on the motorbike, and space is at a premium, and is to hand, wherever and whenever opportunity arises, and its total lack of any zoom is no real handicap! Its been my companion in travel all that while, not my reason for travel, and its small, simple, and lacking 'faff' and is more than second nature to use, I really don't have to 'think' to take a photo with it, its utter instinct. I see, 'something' and the camera is out of my pocket, in my hand, opened, cocked and at my eye, framed, shutter released, closed, and back in my pocket in less time than it took to type it! THAT is what you want in a 'travel' camera. Not mega-pixels and mega-zoom. Something utterly unobtrusive, that doesn't impinge on your holiday in any way, and lets you enjoy your holiday, not waste it, faffing with cameras!
Back to my first question; do you want to enjoy your site seeing, or do you want to spend your holiday prodding buttons looking at a 4" LCD screen most of the time?
Remember, better photographers take better photo's not better cameras. If you are already familiar and comfy with your bridge camera, then you will probably get more better shots of your holiday with that, than you will anything else, especially something new and unfamiliar that dumps you back at the bottom of the learning curve, AND you will get more out of your holiday, seeing what there is to see, not the back of a camera!
On the suggestion of mirror-less systems? I am sanguine. Notion one may be useful to you here is mostly down to them being more compact than a DSLR. But, if you are looking at mega-zooms to go with one? Well, rather defeats the point of an interchangeable lens system camera, doesn't it? Same could be said of a DSLR in fact. You might as well stick to a mega-zoom bridge IF you only want 'one' lens.
If then, you are prepared to sacrifice convenience and compact-ness for the 'versatility' of an interchangeable lens system camera, then 'currently' I believe that DSLR's are the better bet. If you want to explore photographic possibility, the incumbent 'systems' offered by Nikon & Cannon are well established and supported. There is an enormous range of lenses available for them, from the camera makers and the independent lens makers, covering a much wider range of specialist needs, that is far more available and affordable, with an awful lot more on offer second hand, making it even more so, IF you want to delve into it...And that is really the big question. And if you do? Well, I would NOT be looking at spending £500 on a jack-of-all-trades 18-300 super-zoom. I'd be looking at the 18-140, and saving £300 that could be better spent on 'specialist' lenses to justify and exploit having a camera I can change lenses on!