I want to apologize ahead of time, for potentially failing to explaining the problem more accurately:

So I'm attempting to smooth/clean up a design I'm making for a greeting card on Inkscape. I started in GIMP, then realized a vector image would be best, and the trace bitmap function does a lot of what I am looking for.

Rather than explain what I think is happening, I'll just show you the before and after.
This is a screenshot of the .png, zoomed in, and I essentially want the picture to remain as it is, just cleaned up by converting it to a vector



What happens when I perform the trace bitmap, is that it smooths out awesome, but all the colors in the card tend to overlap each other, and show up in places they're not wanted (see how the text now has a small layer of green, and beige?)



And this is just a full sized shot of the card


So Basically, I need to smooth and clean things up, and avoid getting every color traced around the whole image, but stay in their perspective places.

How can I achieve this? I'm new to Inkscape, and have had no luck finding an example of this, partly because I don't even really know the terminology to explain what is happening (apologies!).

Welcome aboard!

A way to do that is to have separate reference images.
For example I would make a separate image with the white lettering and snowflakes over the green background,
and once auto-traced that, ungroup the two and raise the white path to the top (Home) and put the green path to the bottom (END),
and put the rest of the image in between.

So then it would be more focusing on the character.
You could try to export each coloured part as a separate image in gimp,
but that alone would result in gaps between the paths, so you would either need to adjust the raster images,
or use the node editor tool to correct the paths.

Deciding the right z-order would help alot.
By the red part hidden behind the white, you could reduce unnecessary nodes in the final design.

In GIMP you need to posterize the Image into 4 or five colors, that will make the transitions sharp and avoid the antialiasing problems you are having with intermediate tones.
Although you could do it in Inkscape using filters as well, the problem is that you are using a small scale jpg which has a lot of color artifacts. So it's going to take a lot of work with the selection tools in GIMP, subtracting and adding and filling with one color, and some recreation rather than automatic path making. For example, if you zoom in on the snowflakes they're a mess, easier to delete those areas, make a single snowflake and scatter it randomly. And the area under the chin is a mess too.

One way is to redraw the outlines manually over the imported bitmap. If you don't mind the extra time involved, this produces clean artwork. It's not for everyone, but it's good for practice and fun for those who like working with curves.

My alternative way, and please correct me if anyone thinks it's not a great solution, is to create a separate bitmap for each colour you need. Then trace each one separately in inkscape and set the trace to 2 colours. Stack the separate results together and, if necessary break and manipulate the areas as required.

If you trace the bitmap in one go, I believe it is essential to set the appropriate number of colours in the trace GUI. As this can save a lot of messing.

Thanks so much for your help guys!