> ... problem importing graphics.
> ... when I paste it in, ...
Pasting is not "importing", per se. Apart from the provenance issues with copy-into-document, you lose a lot of control over encoding and compression (and for contone images, you also lose any profiles). Pasting from one app to another puts you at the mercy of your operating system's clipboard, which is rarely sufficiently graphics-aware. Clippy will happily convert your nice CMYK, grayscale or bitmap graphics to RGB.
And there's the provenance issue. With paste-in or copy-into-document, future document stewards are apt to have no clue where that image came from, if it needs revising. I've inherited a lot of mystery content like that, and have had to re-create almost all of it (now with traceability).
Store your images in external files (in some common place with a log for extra credit).
File > Import > File [*] Import By Reference.
In the specific case of things that started as line art, if the authoring app generated vector art, keep it vector. Export/Import as PDF, EPS or SVG. You don't have to worry about dpi and pixels with vector art in these formats, because it's essentially infinitely scalable without damage.
If you can't do that, use a suitably high dpi, and a graphics file format that at least supports non-destructive (lossless) repeat-count compressions, like LZW or ZIP. Even the RLE of BMP is better than JPG's DCT damage. For raster images, know what your image pixel dimensions and/or resolution at all points in the workflow. This tends to be a culture shock for those raised in MS Windows, where the prevailing dogma is: you don't need to know, and we won't tell even if you ask. Sorry. You need to know.
Avoid using lossy compressions like that used in JPEG. The "ringing", blurring and stray gray pixels on edges is a classic sign that a curve-matching compression, usually DCT, has been used. Color space reductions, chroma subsampling and other transforms also irreversibly reduce image quality.