Different words capture different senses of this.
conservative - be careful of political confusion. can be adjoined to different words to clarify the kind of conservative you are, eg. "environmental conservative" monitors their waste, plants trees, learns about local ecosystems and industries.
pedant - as in, pedantic. Will fuss over details to finish a task "the right way" or keep things going. Can't stand a half-done job. The meaning could actually work against your favour, in implying you'll waste time to get minor tasks done a certain way, but one can be a pedant about schedules as well and rely on everything being ordered to be efficient.
The answer above of "thrifty" I didn't like so much for the laidback sense, but it does actually answer the question you raised(money).