Coordinate Reference System with units in meters for central Germany?
I suggest to use
EPSG:25832 ETRS89 / UTM zone 32N, because the Gauss-Krueger DHDN CRS zones are based on the old bessel ellipsoid, and you have to apply a datum shift that is not constant over the whole of Germany.
ETRS89 has no datum shift to
EPSG:4326 WGS84 which you can get from GPS receivers, and all official cadastral information has beeen moved to ETRS89 by now.
You could set up a local transverse mercator projection on a center point of your area of interest as well, but that would gain only little improvement on accuracy against UTM.
By the way,
EPSG:3857 has no real meters as units, they match only at the equator.
I'd use whatever is the official CRS in Germany: http://crs.bkg.bund.de/crseu/crs/eu-description.php?crs_id=Y0RFX0RIRE4gLyBHS18z
For posterity's sake, some Gauss-Krueger projection like 31466, 31467, 31468 or 31469 (one per zone). Your town falls into zone 2 (ESPG:31467): http://georepository.com/crs_31467/DHDN-3-degree-Gauss-Kruger-zone-3.html