For me, of the models currently offered, the closest to the Voyage is the Paperwhite (or Paperwhite Signature). Primarily as it still has the bezel flush with the screen the way the Voyage does. The basic Kindle has the screen inset, but, really, either would be a good option. Check out the Kindle page on Amazon and look at the comparison chart for overall differences, though you'll have to go to each product page to see the size and weight specs. (Though, unfortunately, the Voyage size and weight numbers to compare are unavailable as the page is gone.)
The screen size on the basic Kindle is the same as the Voyage; on the Paperwhite the screen is slightly larger, but they've managed to do that without grossly increasing the size of the device - at most it's 1/4 to 1/2 inch bigger in each direction . The resolution is the same on either: 300 DPI which is the same as the Voyage.
The lighting on either of the newer models is the same sort as on the Voyage -- sort of a side lighting. The Paperwhite has more lights than the basic model, and you can adjust the 'warmth' -- from bluer to yellower as you prefer. If you like the auto-adjusting feature of the Voyage you'll want the Paperwhite Signature.
Buttons are right out.

None of the current models have either physical or 'haptic' buttons. You just touch or swipe to turn pages.
FWIW, I still have and use my Voyage, though I do notice it doesn't respond as quickly as my Paperwhite. Not sure if it's slower than it was, or just slower in comparison! Reading is still just fine -- it's just that manipulating the menus/catalog is a bit laggy sometimes. It still holds a charge decently. I keep a micro USB around to charge it -- it and my Oasis are the only devices I have left that use that sort of connection. The new ones are all USB-C.
As to ads, they all come with or without the ads, you just pay extra for 'without'. Note that you can 'buy out' of the ads later if you get one with them. Some people do that when the ad-supported ones are on sale but the ad-free ones are not, which has happened occasionally. More often it's availability on initial release: you can often get one with ads right away but may have to wait a few weeks for ad-free.
And, speaking of sales, Amazon's Prime Days are next week -- the 16th and 17th. I'd wait to purchase anything until then as they'll likely be on sale. You may also be able to trade in your Voyage -- probably won't get much more than $5 or $10 for it -- but there's often a program where you can also get some credit for a new kindle. O'course, you might want to keep the Voyage just for nostalgia.
I've not mentioned the Scribe at all as it's a much larger device, but also quite nice if you want that size.