Note too that the shorter the zoom range you go, the better the distortion control tends to be - it's much easier for a lens manufacturer to correct for the specific image quality issues in a very small focal range than it is over a larger range. The 16-105 should be better, but a shorter range might be better still. Of course, a prime lens will usually be best overall, since they don't have to account for moving optics. If you know for sure that wide shooting is something you need, it might be best to look for the shortest zoom or nice prime that suits your needs there. Same goes for the telephoto range - the less focal range, often the better the optics and specific distortion/flare/IQ corrections or issues.
Personally, I absolutely love the 18-250mm lens - and it's my go-to travel and all purpose lens. But I also have 4 primes and 3 other zooms that have specific duties to cover most-needed focal lengths when I know what focal I need and want maximum quality.
As for bodies - the A5xx series cameras have excellent sensors and feature content - they aren't a7xx build quality or have the higher-end weather sealing or such, but they do have better low light performance and faster focus motors and excellent accuracy, plus some nice newer features not available on the A700 - so where you may lose out a bit on the overall semi-pro build and weatherproofing, you make up for it in much lower price, better sensor performance, and very nice feature improvements and additions.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 200-500mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony NEX5N / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / Pentax K adapter / Konica K/AR adapter / bunches o' Konica & Pentax lenses!