I've recently upgraded to a Nikon D3400 Single Lens Kit (18-55mm) from a Pentax Optio A10. Aside from family photos, I would also use the Pentax take photos of DVD cases (for listing on ebay) using the macro setting. To avoid the flash obscuring the text on the case, I would take the photo at a angle to the surface on which the DVD rests. The photos with the Pentax were ok (better than my phone) but a little dark so I'd change the brightness and contrast in GIMP. I've tried to take the same photos with the Nikon but the text at the top and bottom of the case is blurred with the macro setting. I've experimented with different aperture settings and I found the smallest aperture with the 35mm zoom setting seems to work a little better. Do I need to get a different lens?
To avoid the flash obscuring the text on the case, I would take the photo at a angle to the surface on which the DVD rests.
Sounds like you're probably using the built-in flash on your camera. A better solution would be to take the photo straight on, and arrange the illumination so that the subject is lit from an angle. That might mean using an off-camera flash unit, or just some constant light source. DVD cases aren't known for moving very quickly, so you can trade shutter speed for light intensity and get a decent shot without a lot of light.
Since you're taking photos for eBay listings, what you probably want is a nice plain background with diffuse light. A small light box would be ideal for this kind of thing. You can aim a few cheap work lights at the sides of the box, put the product inside, and get good lighting for your product with little effort. You can use off-camera flashes in place of the work lights if you want, but you don't need to go to that expense.
I've experimented with different aperture settings and I found the smallest aperture with the 35mm zoom setting seems to work a little better.
Yes, smaller apertures will give you more depth of field. Smaller apertures also reduce the light available from the flash, so there's a tradeoff there.
Do I need to get a different lens?
No. A typical kit lens should be fine for what you're doing. Look into different lighting options first.
When doing close-up work, you need to keep the camera square with the subject. This is because the range of sharp focus, near-to-far, is super shallow. We are talking about depth-of-field. This is what we call the range of acceptable focus. Your approach is wrong! Instead of angling the work to avoid glare from reflections from the flash, you should change the method you are using to light the subject.
First try to do your imaging outdoors in open shade. Open shade is that area shaded by a building or patio cover or umbrella. If open shade does not work for you, than construct a highly diffused indoor lighting setup. I suggest “tent” lighting. A white sheet or a white translucent plastic panel from the hardware store will do the trick. Place some LED lamps above this diffuser and Voila! You have created a defused lighting setup.
You might still get some unwanted glare, but this can be mitigated by mounting a polarizing filter on your camera lens. Once the polarizing filter is mounted and you are using continuous lighting, you control glare and reflections by rotating the polarizing filter. These filters screw into the front of your lens, however, they are loosely attached, so you can rotate them as you focus and compose.
The rotation allows the polarizing filter to be adjusted by you so that you get the maximum effect. It won’t do you any harm to look up polarizing filters on the internet, so you can better understand how photographers use then to alleviate reflections.
You can try using your lens on 55 mm and f9 or f8 aperture. This should give you enough depth of field for your shots.
If it is not enough, try not to take the photo at an angle but rather parallel. You won't be able to use the built in flash as you will get reflections but try using natural light(for example shoot in front of a window).