Upgrading wheels will make quite a difference, the weight in the wheels rotates and takes a lot of power to keep them rotating. Loosing weight off the wheels and tires you use, will make a lot more difference than upgrading things like a stem, handlebars etc.

I have recently built up a 9.5kg hardtail, in comparison to my 12.5kg anthem it climbs like a dream. A major difference is that the wheelset and tires are significantly lighter, as well as the more efficient power transfer without rear suspension.

So my advice, upgrade wheels but you can slowly upgrade other parts if you feel like it later.