So i want to get a new laptop but I want to get something that's actually an improvement.
My previous laptop specs were
Radeon 7570m dedicated gpu
16gb of ram (I kept the ram for my next laptop)
500gb hdd + 500gb ssd (kept ssd).
Is there any laptop under 600 new and/or used that's an improvement over my previous?
You're not likely to find anything "new" with an i7 *and* a GPU.
The problem with 4th through 6th Gen mobile i7's (for the most part) is they dropped to dual-core w/HT.
Really depends what you want to use the laptop for. If for strictly gaming, a modern(ish) i5 would allow you to net you a pretty solid 'boost' over your current GPU offering, in roughly the $600 range (+/-10%).
*****If you look to something ~6th Gen, you should be able to reuse your DDR3L, but anything beyond that is going to require DDR4 - you could sell the DDR3L though, to facilitate the upgrade to 16GB DDR4. Anything remotely in your price range is going to ship with 8GB + GPU. If you want 16GB from the outset, you'd likely sacrafice the GPU****
Any i7 with a starting number greater than 3 and ending in something like HQ.
Pretty much any GTX 10 series card is going to destroy any older generation mobile GPU. There should also be AMD Vega mobile GPUs hitting the market, but these are still going to be brand new and expensive I imagine.
You won't be able to keep your DDR3 / DDR3L memory, newer systems are DDR4. Any laptop that takes DDR3 is going to be something like a 4th or 5th generation Intel CPU. Though nothing says you couldn't find a used top of the line system from that era with a GTX970m or something.