German R Sound

So I got made fun of for accidentally aspirating the k in Markt (we were joking about old American German newspapers and I said "Tja, fuenf Dollar dass wir das Wort Pferdemarkt finden werden.") and making it sound like Macht. I learned German from people from Niedersachsen and Bremen and have an apparently noticeably light pronunciation of 'r' so that gar is "gah", werden is "veh-den", and wieder is "veeduh". I don't know how to write the way I pronounce it; it sounds a lot like uh or eh but it's held longer and has a turn to it. I don't really notice that I don't pronounce the 'r' sound.

How strong is 'r' supposed to be in spoken German?