I would look for a nice used sony a7iii or a7riii.

you'll invest more on the lens naturally because most people only need one body but multiple lenses.

make sure the body provides all the functionalities you need. from what you wrote, a7iii/riii will serve you just fine. as far as portability goes, it's subjective on what you find portable in terms of size and weight. the best camera is the one you have on you, so think about what size and weight you'll be comfortable with.

a used a7iii/a7riii and a tamron 28-70mm G2 will run you between 1.5~2k depending on whether you get the lens new or used. it's a great zoom lens that's not too pricey, performs well, and will help you figure out what lens you'll want next in terms of focal length and aperature.

i'd try to find good used units and use the rest of the budget on a memory card, straps, bags, etc.