Lots of people here suggest buying a new camera, but I might pitch in and say that it might be good to buy second hand. With a limited budget you can get much more value for money. I think (especially for beginners) camera technology hasnt changed very much since about 2012, and you will get the same quality pictures out of most of those, than a modern one in a lot of cases. Also, if you are serious about being in photography you could get an older semi-pro body for the price of a new entry level DSLR. The increase that you get in control and robustness is well worth giving up any possible increase in quality in my opinion.
I myself was in a very similar position as yourself 3 or so years ago and have chosen the second hand route for the reasons mentioned above, and I do not regret doing it.
For me I bought a DSLR since I dont mind the weight so much, but there's plenty of terrific mirrorless options out there too. If you have smaller hands, I'd definitely recommend the Fuji XT100, I have seen them for bargain prices second hand.
If you do decide to buy a new camera, I second what andrewc posted in that I would get a package with lens included. Some of the 18-55 lenses are very good out of the box. Then analyze your shots after using it for a bit, and determine what your next lens purchase should be (if most of your shots are 55mm and you want more reach, get a tele, if most are 18 then maybe a wide angle is nice, if you'd like a bigger aperture, get a 17-50 2.8 or a fast prime)
I definitely wouldn't buy a whole arsenal of lenses to take with you traveling, first of all because you have no clue what they are, how they act and how to use them. But more importantly, you'd probably not use them at all. On my APSC camera during traveling, I pretty much solely use the 17-50 with the exception of night pictures for which I use a 35mm prime. Only for special occasions like going to a zoo do I bother to pack a zoom.