My honest advice is don’t worry about the old lenses. Any camera should come with a comparable lens to the 18-55, and the 55-200 is not anything to base camera choice on. The only compact cameras that can properly use those lenses will be Canon’s discontinued EOS M series. It is a totally dead end system which has ceased development. I don’t think your lenses would work on the crop bodies of their new system, but the difference in price would make it a bad choice anyways. You can technically get an adapter to use the lenses on Sony’s cameras, but they will not work quite right in my opinion, will probably work much slower, have focus issues, and maybe even have issues with the stabilization causing blur.
That being said, I really think the Sony cameras would be the way to go, but look at the used market. At least in the US, Sony made so many cameras that the used older models go for a lot less money, so they are really cheap to pick up. The A5100 would be a great balance of small, good image quality (24MP), and I assume very cheap. The A6000 line would add an eye piece but be larger. The A5000 would be good but lower resolution (20MP), and the entire Nex line are older yet and mostly cap at 16MP. The 16-50 lens is super tiny when off, and in my opinion a very under rated lens.
My honest advice is don’t worry about the old lenses. Any camera should come with a comparable lens to the 18-55, and the 55-200 is not anything to base camera choice on. The only compact cameras that can properly use those lenses will be Canon’s discontinued EOS M series. It is a totally dead end system which has ceased development. I don’t think your lenses would work on the crop bodies of their new system, but the difference in price would make it a bad choice anyways. You can technically get an adapter to use the lenses on Sony’s cameras, but they will not work quite right in my opinion, will probably work much slower, have focus issues, and maybe even have issues with the stabilization causing blur.
That being said, I really think the Sony cameras would be the way to go, but look at the used market. At least in the US, Sony made so many cameras that the used older models go for a lot less money, so they are really cheap to pick up. The A5100 would be a great balance of small, good image quality (24MP), and I assume very cheap. The A6000 line would add an eye piece but be larger. The A5000 would be good but lower resolution (20MP), and the entire Nex line are older yet and mostly cap at 16MP. The 16-50 lens is super tiny when off, and in my opinion a very under rated lens.