Gaming laptops are cheaper than gaming desktops
The most misunderstood subject ever. And NO, A gaming laptop is never less expensive than a gaming desktop.
Well, let's see, when it comes to gaming, we are talking power, sheer power. A desktop can deliver for you MUCH more power for a lower price. You can build a seriously powerful PC for just 800$. I say JUST 800$ because for the same amount of money you cannot hope to achieve the same performance.
On the other hand, laptop's only advantage is mobility. A desktop will remain where you put it and you cannot take it with you.
So in short, if you want performance go desktop. If you want mobility go laptop.
Now what I would suggest is definitively a gaming desktop no doubts about it.
If you make up your mind take a look at the forum, there are many open topics that discuss desktop builds and if you don't manage to get an answer just tell us here. We will help you build one again.
And in case you need more detailed help or have more detailed questions just PM me and I will prove as much help as I can