I'd lean you in the direction of a low-end DSLR and avoid the compact or bridge cameras. Here's why...
The camera body simply needs to be "sufficient" to the task. More important are the lens choice... and even more important than the lens is the lighting. As soon as you get into lighting, the DSLR becomes the only "real" choice.
You can't create good "light" without good "shadow". It's the shadow & highlights that oppose each other which create the 3-dimensional detail that ours eyes pickup. If the lighting is "flat"... no highlights... no shadows... then the image looks 2D and far less interesting. But getting this 3-dmensional look requires that you get the light OFF the camera.
You could start with natural lights... taking images near large sources of light (big windows, etc.) and you can supplement with low-cost photographic reflectors (shiny fabric on a collapsible spring hoop) and this would allow you to control the light and shadow providing you have a good place to shoot.
But you can up the ante with flash (strobes). And you can get extremely creative with strobe placement... to illuminate the subject from the sides and soften the flash by using a broad diffuser (soft-box or shoot-through umbrella) which makes the light source seem very broad rather than pin-point (pin-point light sources create shadows with hard-edges which aren't as flattering.) But since you're shooting glass... you may even want to back-light the subject to give it a nice glow.
The problem with point & shoot and many bridge cameras is they lack an attachment point for external flash -- all DSLRs have a flash "hot shoe" and this can be used to trigger off-camera flash using wireless triggers (the trigger mounts to the on-camera hot-shoe and is used to tell the off-camera strobes when to fire.)
The camera itself does NOT need to be a high end DSLR. You'll be shooting a non-moving subject and you'll probably be using a tripod. When the camera isn't moving and the subject isn't moving, you can take all the time you need to get the shot right. You don't need a camera with lots of focus points... nor a blazingly fast continuous burst-speed to blast through 10 frames per second, etc.
For what you want, a Canon T3 or T5 (and these are their low-end entry DSLR models) would be fine. Even the kit lens would be fine. If you want very fine close-up detail, you might consider a macro lens (for a Canon, I'd look at the EF-S 60mm f/2.8 Macro USM... but I would't suggest this right away... get a feel for using the camera with it's "kit" lens first.)
All DSLRs (Canon, Nikon, Sony, etc. etc.) have a fully-automatic shooting mode in which they are as easy as any point & shoot camera. But the reason people tend to prefer the "look" of a DSLR photograph over so many others is because when you start controlling the light, angle of view, and depth of field, you can get some exceptionally beautiful results and you can use this to work emotion into the photograph... if you want something soft and dreamlike... or hard and edgy.... you can do all that. But getting these shots means you eventually learn to take control of the camera... get it out of fully automatic mode, and learn how to control an exposure.
I would look at a Nikon D3xxx series (that's Nikon entry-level bodies) or Canon's T3 or T5 (that's Canon entry-level bodies.) I can't offer specific Nikon advice since I'm not a Nikon shooter, but frankly you'll find that any entry-level DSLR on the market will be able to get the results you want... and at that point it's more about you learning to light and shoot creatively.