Well I have been using GIMP and the occasional bit of inkscape for most of what I have been doing but hey. Some of the photoshop peeps dislike gimp and it is not MS office vs Libre office of much the same capabilities (photoshop is very much the superior program) but you can get most of the way there on gimp, especially if you think through things (photoshop's layers as undo history thing is great, nothing stopping you from making a new layer in gimp though).
+1 to phlearn
https://www.youtube.com/user/PhlearnLLC
They are a soft sell for a paid tutorials site but I imagine you have probably teased out the contents of a paid journal article before from free abstracts and whatever else before now. Same difference really.
The above is an example of them at their best. They also released one of their paid tutorials (a star wars themed one)
Tools I like/ones I wish someone had sat me down and shown the power of as the first things they did
Layer masks
Quick mask, mainly for when use the feather selection command (it keeps everything but the edges become less selected so do not end up with as sharp changes)
Right click layer -- alpha to selection
Layers in general. Do also play with layer types and general opacity.
http://www.fontsquirrel.com/ New fonts are great, even better when they are free.
Gaussian blur -- alpha to selection, new layer, fill with some colour, select everything, gaussian blur and bam you have a nice glow in whatever colour you picked around the item you want. You may also want to throw in an increase selection size in there, alternatively fill it in with black and drop the opacity of your new layer and you have a nice shadow.
Paths. Magic want select is great, paths are godly. Ninja tier is using the existing image to generate a layer or something you can use to refine a selection.
Lately I have been looking at all sorts of text effects I can try, however after I learned to think using the above things I have mainly been watching things like phlearn and thinking my way through converting them to Gimp (not actually that hard for most things). As part of the text thing I also see something I like the look of and then try to replicate it, or replicate it by with my chosen text or colours. There are examples of people that know this sort of thing everywhere though, adverts, logos and album covers seeming to provide most of what I want to play with.
Another thing I like in Gimp. If you have a font tab up then right click it and press render font map, select the options and a few seconds later you can have your chosen phrased rendered in up to every font on your system. Quite nice for stylistic stuff or font matching.
Edit. Like a fool I forgot to mention clone brush, heal brush and the classic photoshop make tits bigger and love handles smaller filter.
Clone and heal do much like they and copy parts of an image to another part and try to make a mixture of the two for heal. Press crtl and click somewhere to select the donor section, it will move if you drag your mouse.
The bulge and shrink command in gimp is called iwarp and if you select filters -> distorts -> iwarp you get there. It is not that refined (no zoom, no undo in the command itself beyond a full reset) but select what you want to edit beforehand and you can get somewhere. With both programs you will find you probably want a bigger brush than you think you do.
I did also pick up a little drawing tablet. It is great for handwritten text and tracing things where you need a hand drawn look but I am not quite sold on it being almost mandatory as some would claim. That said if you can pick up an old wacom branded thing in a second hand shop for $60 or so (make sure it has a pen) then I would consider it.