I've never used a pressure barrel before, but from what I can gather, its just like making a huge bottle of beer. Your steps look ok from what I can see. Here's my suggestion.
1. Finish fermenting beer
2. Sanitize anything touching final beer - barrel, tubing, racking cane, spigot
**3. make a priming solution
Boil 1-2 cups of water for a few minutes. Add your desired amount of priming sugar to the boiling water to dissolve and boil for a few minutes.
**4. Add priming solution to barrel
5. Transfer finished beer into barrel
(adding the priming solution helps to ensure even distribution of the sugar into the beer. In the case of a pressure barrel, I think the biggest advantage is to make sure the sugar is dissolved so it doesn't just clump at the bottom)
6. Wait for yeast to digest sugars and make carbonation. This can take anywhere from a few days to a couple of weeks. Warmer conditions will help this occur faster.
7. Chill to serving temps.
I'm going to assume that you are in Europe? In the US, "pressure barrels" aren't widely used, so please, if anyone sees something glaringly wrong, feel free to correct.
I think the other thing to keep in mind is that since this is a closed system used to create carbonation in the beer, you must ensure a good seal on all possible areas where the CO2 could escape (spigot, lid). You may want to use some kind of lubricant/sealant like keg lube to help. Also, be very careful as in theory, depending on how much sugar is used, you can create a lot of pressure inside the barrel. Make sure it can handle the load you're intending to put into it! Congrats on the first brew