Your lenses (and the N6006 / F-601 body) use the Nikon F-mount, one of the longest-lived and supported lens mounts ever. It has gone through a few updates over the decades, in order to support features such as autofocus, fully electronic aperture control, etc.
Your Nikon AF lenses use Nikon's original screw-type autofocus. Your generation of lenses were shortly followed by so-called "D" lenses (AF-D). Your lenses are often referred to AF (non-D), but the "D" distinction doesn't really matter. As far as Nikon camera body compatibility is concerned, AF (non-D) and AF-D lenses are the same.
Nikon publishes and updates their Lens Compatibility Chart. The takeaway from the chart is that your lenses will work with any Nikon DSLR you attach them to. The only caveat is that on low-priced consumer-targeted DSLR bodies, those lenses will not autofocus. Other than that, all of your lenses will work perfectly on any Nikon DSLR.
All of the lenses have a manual aperture ring without (as far as I know) any possibility of giving aperture control to the camera.
Actually, that's not true — any Nikon DSLR can control the aperture of any of these lenses. Nikon's F-mount uses a lever-actuated aperture control from the camera body, even with lenses with an aperture control ring. In order to let the camera control the aperture, all you need to do is turn the aperture control ring to the smallest aperture (i.e., the largest F-number printed on the lens) on the left end of the aperture dial. On your 50 mm lens, it's the "22" in orange; on the 105 mm lens, it's the "32" in orange; on the Vivitar lens, it's "22" (but I don't think it's marked by any color). By setting the aperture to the smallest value, this provides the full range for the camera body to move the aperture control linkage.
Image Sensor Format
When talking about DSLR bodies, you will often see the distinction between "full frame" and "crop sensor" bodies.
Full frame refers to 35mm film equivalent frame size (24 × 36 mm). In Nikon terminology, these are "FX" bodies.
Crop frame, crop sensor, APS-C refers to sensors that are 1.5 times smaller than full-frame, measuring approximately 16 × 24 mm. Nikon labels these bodies "DX".
The smaller sensor area of crop sensor bodies provides a narrower field of view than you would see in a full-frame body, using the same lens. This change in field of view is related by the aforementioned 1.5× crop factor applied to the lens's focal length. Thus, your 50 mm lens, when mounted on a Nikon DX body, would have the same field of view as a 75 mm lens on a FX or film body such as your N6006.
In short, all of your lenses would have slightly more apparent "reach" when mounted on a DX body.
Camera Suggestions based on price
In general, DX bodies are less expensive than their similarly-featured FX counterparts.
Searching MSRP for new camera bodies only (no body+lens kits), I don't think any Nikon body will meet your price requirements. As I mentioned, the lower-priced consumer targeted Nikon D3xxx and D5xxx series bodies (all of them DX) will not allow your lenses to autofocus. For that functionality, you would need to step up to a D7xxx series (also DX).
At just under $500, you can get a D3500 with 18-55 mm kit lens.
I would recommend finding a refurbished or used D5600, or if you're lucky, a well-priced D7500. These are the current latest models in their respective product lines. More recent inexpensive DX lenses, including the typical 18-55 mm or 55-200 mm kit lenses, are fully autofocus-capable, and will quite often come with a body you find on the used market.
When searching for camera bodies, to get a reference of new MSRP prices, I'd start with photo/video sites like B&H Photo/Video or Adorama. I don't have any specific recommendations for finding used gear, but both of those sites often have refurbished gear.