First thing that you need to find out is how old the Artex is; if it's very old, it might contain asbestos and then you are into a completely different ball-game.
Artex can be steamed off or removed with a product such as the one you quote - but, either way, it is very messy and at the end of it you might not be left with a surface you can paint without further preparation work (papering?). You can skim over but this might be difficult if the 'patterning' of the Artex is very irregular. It might be quicker and easier just to board over it and re-plaster but an already low ceiling might militate against that.
I wouldn't particularly call it a DIY job unless you are very good at DIY - and if it is old and contains asbestos, you're not going to be able to DIY. The only way to get a real idea of the cost is to get a two or three builders in to suggest their solution to your problem and give you a price.