We have a burner for wood only, but have successfully also burned peat in it. We had a log burner in our last house and we both also grew up in homes with open fires.
Unlike an open fire, a burner is much safer and can be easily left unattended to burn overnight or when you are out the house. You can move the controls to restrict the air flow, so that the coal / wood burns very slowly and doesn’t completely go out and it will continue to radiate heat.
You can also get special briquettes (made from either coal or compressed wood shavings) that are designed to burn very slowly all night. This saves you having to relight the fire the next day, as you would just add more fuel to it and open up the controls to get the fire going again.
We tend to light ours mainly at weekends in the winter and in the evenings if we are going to spend time in the living room where it is located.
You can buy the quick light logs from home bargains, which are easy to use - light the paper and it can burn for a couple of hours - a quick and handy fire that can be lit when getting in from work for example.
Have you just had the stove installed, or moved to a house where it has been installed? Either way, make sure you get regular chimney sweeps carried out.
It may take a bit of trial and error to get used to your particular stove, as size and design can determine how they burn. I would also check that you can burn actual coal like in an open fire, or if it has to be the egg shaped coals that are like barbecue briquettes - (smokeless ovals I think they’re called) depending on the stove and if the property is in a smoke free zone, you may not be able to use regular coal.
If you are buying wood, get a mixture of kindling and logs, but make sure they are kiln dried as they burn better and cause less residue building up in your chimney. Again, Home Bargains can be good for picking up bags of kindling and logs, at least until you sort out a delivery of wood / coal.
If your burner has a multi fuel grate, you should be able to use both at the same time - e.g. set the fire with kindling and then add coal / wood on top.
You will get a feel for what works best for your own stove, your family and your house needs, it also depends on the age of the house and the weather - good luck!