So, here is a compare-and-contrast of the two ways of starting off when crocheting in rounds:
Chain and slip stitch
This kind of starting loop is quick and easy, especially for beginners. If you run the end under the first round of stitches you don't have to sew the end in. It won't pull open.
However, depending on how many chain stitches you start off with, you either have a gap in the middle or a very tight space to fit the hook into. The hole is not adjustable after it's made. Sometimes you also have a lump where the slip knot is.
This photo shows one of my daisies. The starting loop was four chain stitches joined with a slip stitch. I worked the next round of stiches over the top of the yarn end so I was able to simply snip it off without a darning needle in sight!
The size of the hole is adjustable to fit the number of stitches in the first round. The hole can be pulled completely closed, ideal when making a toy that will be stuffed. It has a very neat finish.
However, the end has to be sewn in. The loop can pull loose over time if not sewn in firmly enough. It can be tricky to master because you have to hold a loop of thread in place with your finger and carry on crocheting at the same time.
This photo (of Levi the Elephant's backside!) shows just how lovely and neat the magic ring can be.
Here is a video from my YouTube channel to you how to crochet a magic ring. It is my first ever YouTube crochet tutorial. I hope you find it helpful.
And in case you were wondering, here is a picture of my marvelous invention for holding my phone while recording the videos. I'm quite proud of my resourcefulness :-)
To see what other people thought my homemade tripod might be, have a look at the comments on my Facebook page here.