1x1x1, finally a rubik's cube I can solve.

Nice! I'm in the same camp, just for fun.

My tip for the megaminx is that all the algorithms are the same as the 3x3x3, they just go off at weird angles. If you can keep your focus on a corner and treat it like a 3x3x3 you should be good. The last layer is odd to get the edges, I use the same algorithms, but the patterns to look for are different and the edges move a little differently since there's an extra edge that moves around. The corners are pretty easy in the middle portions, so I just put them in place while being careful about the completed parts.

That one's a dodecahedron

What happened to the 'Rubik's' part of the Rubik's cube in this community name, description, and this post? Only seen it mentioned in one comment.

I have that same Megaminx, it's a good one! I'm also not going for records etc. I don't even time myself doing the mega -- it's more for stress relief when I don't feel like trying to break my 3x3 records. I basically used a pdf of instructions to do the megaminx beginner's method, until I had it memorized. It's basically all F2L until you get to the top layer, then there's a couple of simple algs (sune, etc.) to memorize to do the top.

This megaminx is a classic

Nice!

4x4x4 is the next logical step, but megaminx is actually easier: no new algorithm is needed (if you come from the "beginner method"). Figuring out all layers (except the last one) is pretty easy. Then I suggest you do some 3x3x3 algs to see what is affected. Anyway, that’s what I use too, no world record in sight either!

4x4x4 parity is the real hassle. I use commutators to remember it, and it’s pretty inefficient too :p

Where did you buy them?