The purpose of a trench edging is to keep the weeds and grass from spreading into the flower bed. Roots won't bridge a vacant space.

With this in mind you have to evaluate how deep or wide it should be. It should be deep enough to keep roots that grow under the soil from crossing over. If you have only plants that spread, like your st Augustine, on top of the ground then it needn't be deep at all, just deep enough to keep the roots out. You should have at least 3 or 4 inches of space between the grass and flower bed. This is not as much as it sounds, because the flower bed slopes toward the lawn

To make curved lines--lay down the garden hose in front of the bed. Move it around and in and out until you have a line that is pleasing to the eye. Then take an edger and scribe the line. Do the same thing to make a straight line but use a board or pole or something straight to mark the line.

An edger is a good tool to buy if you are going to have trenches. A quick trip around the beds with it a couple of times a year will keep your line crisp.

As far as mowing --simply keep most of the mower on the grass. We have never had an unsightly look to the edge. I don't care if it is cut lower there because it will keep the grass from spreading.

As for removing weeds and grass from the beds. You can dig them or spray with round-up. Be careful with the round-up because it doesn't recognise the difference between a weed and a flower and will kill both. A big piece of cardboard held in front of the flowers and spraying low to the weed will help overspray.

I hope this helps