I am wedding photographer and I also travel or walk around to shoot for fun
I have 70-200vr2F2.8, a very good lens, but I can say, with this focal range...really seldom use...
Roughly I can say, this lens, contribute less than 5% of my trip photo...
Really dun think is a good idea to get the 70-300 by paying so much additional
(Unless you want to get it and sell it directly)

If really want a lens that able to cover most of the scenario during travel, 18-135 (around this focal will do) is the best

If want nice bokeh, quality photo, need get fix aperture lens such as 24-70F2.8, 16-35F4...etc, but I think this is too much for you at this moment, too expensive

Another option of nice bokeh and quality is get prime lens, but you need to get the prime that with motor (D5XXX series cannot drive prime that without motor)

By seeing your usage (fun and hobby), get D5600 with kits lens(around 18-135) meet your needs
But, kit lens usually cant produce outstanding nice bokeh photo
(you might been inspire by some photo online that tot of getting any DSLR then can produce that kind of photo, I am one of the victim last time...)

Ofcourse, you can buy other brand such as Canon, but if possible, stick with Nikon or Canon, easier for you to sell it off when you quite photography next time(If)

Have you ever think of get Mirrorless? Mirrorless such as Sony A6000 is having DSLR sensor as well, smaller body, and light. From what I see from the pass Thaipusam at Batu cave, many user change to use mirrorless already.

DSLR always fit better with hand, but it also more bulky
If do street photography, when you holding a DSLR (no matter how small it is), it will attract people look it you and feel not so comfortable
However, with compact/mirrorless/phone, most of the time, people may just ignore of what you are doing

I carry a powerbank with my A6000, then I can shoot for whole day and no worry of low batt

Talking about 70-300, with D5600, crop factor of 1.5, that focal range, I really seldom will use with this focal

Imagine, I go travel with friends, when I want to help them shoot photo (travel photo), 70-200, I need to stand very far, so that can snap people with landscape together

When friend just next to me, I cant shoot her/him, too near....I need to walk far....

Yes, some scene see from far is nice, then can snap with 70-200, but, it only contribute about max 5% of my whole trip photos

70-300 is not a high demand lens, most probably u can see people selling online e.g. RM1500, but this is just a price, doesnt mean got people want to buy

What you may can do is, u can PM KLDSLR of ask him how much he can offer to take your lens (70-300)

My advice is, just get a camera that meet your needs will do. So, you must know what you want to shoot first....

Last night when I shoot for a dance performance show, I met a guy that using D5100+ 18-55
He is just a beginner and ask be of what setting to use

Of course, when I try to explain the aperture, shutter and ISO to him, by using his camera
I find out, when my aperture is F5.6, 55mm, I already push the ISO to 3200, but I still cannot get shutter that faster than 1/100
The photo come out still dim and of course, when slow shutter, photo turn to be not that sharp due to hand shake

By looking at this, getting a 70-300 that with dynamic aperture, I can say it not much useful during dim light environment (if not shoot with tripod)
My personal opinion, dun get the package that come with this 70-300 (then you sell it)
Just get what you need will do

If really plan to get D5600, I would suggest just get the body + kit lens (such as 18-55, 18-120) and not more than that, or with some prime lens also another good idea

When travel, I use D750+35mm and also I will bring along my a6000
my a6000 mainly is for video purpose, and some place as market or shops
Because these places if u bring out your DSLR, people will be shy or run away or trying to avoid you
But, if you using phone or mirrorless, people can accept.

The response and handy feel of DSLR is something that Mirrorless cant reach at this moment

So, you have to think back your self what you need, then only can spend wisely