JPEG Quality of 9 ~ 10 out of 12 (or 70 ~ 84 out of 100) is pretty indistinguishable from uncompressed. See this article for an in-depth comparison. In short, if you have less color gradients, you can get away with higher compression (lower quality values).
For PPI (what you care about), in general, 240 to 360 PPI is high quality. This depends on typical viewing distances and your audience. For example, with posters where people won't be walking up to and scrutinizing, you can get away with lower PPI because the viewing distance is further.
Ideally, you should find out what the printer's native PPI (not DPI) is and use a quality program and algorithm to resize (including upscaling) to that resolution, as opposed to letting their software or printer do the resizing.
To calculate the number of pixels, simply take your desired physical output size, convert to inches if necessary, and multiply by the PPI:
10 cm by 15 cm x 1 inch / 2.54 cm x 250 pixels / inch = 985 pixels by 1477 pixels
10 in by 15 in x 250 pixels / inch = 2500 pixels by 3750 pixels