If the sink is a 1-1/2" drain then the vent should also be of the same size. As far as the distance to your main stack and the number of elbows and 45's, this really varies all over the country. Each county and town relies on their own rules and they supersede any national standard. If this does not concern you then go for it and hope all of your neighbors like you (these are the people who turn other people in).