If it says the gauge is 15 sts = some amount I would cast on 19 stitches. I like to have a couple on each side over the ones that need to be measured because the edge stitches get distorted and don't give an accurate gauge.
As far as the row gauge goes, what you say is right. 20 rows should = 4 inches in that direction. But row gauge is usually not that important and it is pretty hard to control. If you get st gauge and row gauge is off if you try to fix it you'll mess up the st gauge.
You can usually work to a certain length and just ignore row gauge. In some patterns everything is given in rows instead of inches but you can figure out mathematically how to adjust it in most cases. Use the gauge they give to figure out how long they are making something and then using your own gauge figure out how many rows you'll need to get that length. Sometimes it is more complex if the pattern is very dependent on having a certain number of rows, like for a complicated cable pattern with lots of rows.