New to Speedcubing, What Method to Use?

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Hey! I want to start speedcubing. I just bought a Dayan Zhanchi 2x2 and 3x3, and can move them pretty quickly. I want a good method to solve them fast (I currently use the beginner method, solving in about 1:20.00). I've looked at Adam's method, the Fridrich method (standard and intuitive), and a few others, but I either can't grasp the concept, understand the tutorial, or can't learn all of the algorithms. What's a good, easy, and fast method to solve the 2x2 and 3x3 cubes with (preferably) less than 10-15 algorithms to memorize? (I'm horrible at memorizing algorithms.) I like video tutorials or ones with a lot of pictures. I am a very visual person. Puzzles I can currently solve and their averages (all using basic methods): Pyraminx [16.00], 3x3 [1:20.00], 2x2 [25.00], and Megaminx [8:00.00].

Thanks!

EDIT: The Roux method seems to work great for me until the edge placing. From there I can't understand what it's trying to relay to me. If you suggest the Roux method, can you also explain the edge part (step 4)?
 
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Thank you guys for the good and quick responses! I've tried out a few Roux solves and it works great for me! It has my thinking style, few algorithms, and it can be fast. I think I'll go with Roux. Once again, thank you!
 
Edit from over a year later: I now use CFOP. I was about to approach 40 seconds with Roux, then eventually switched to Beginner's because I suck at blockbuilding. I average sub-30 now. I almost have a 1-look PLL. I have a 1-look OLL, but I kinda cheat because I orient my edges during my last F2L slot using some basic ZBF2L algorithms. As far as 2x2, I use Ortega with TOLL. I average sub-5. I use Moyu white cubes (Aolong and Lingpo). Pyraminx times have only gone down to about 10 seconds because I so rarely solve it, but I'm now very actively learning 1FLL and FP to speed that up to sub-6 hopefully. I might learn 2FLL and 3FLL, but I'm skeptical about its effectiveness. 1FFP would be really cool though. Megaminx times are still about 8 minutes because I, quite literally, never solve it. I use a 6+LLL with Beginner's and intuitive techniques.

I sometimes solve my 3x3 with Corners-first, ZZ, Petrus, Roux, and SBS just for fun.
 
Edit from over a year later: I now use CFOP. I was about to approach 40 seconds with Roux, then eventually switched to Beginner's because I suck at blockbuilding. I average sub-30 now. I almost have a 1-look PLL. I have a 1-look OLL, but I kinda cheat because I orient my edges during my last F2L slot using some basic ZBF2L algorithms. As far as 2x2, I use Ortega with TOLL. I average sub-5. I use Moyu white cubes (Aolong and Lingpo). Pyraminx times have only gone down to about 10 seconds because I so rarely solve it, but I'm now very actively learning 1FLL and FP to speed that up to sub-6 hopefully. I might learn 2FLL and 3FLL, but I'm skeptical about its effectiveness. 1FFP would be really cool though. Megaminx times are still about 8 minutes because I, quite literally, never solve it. I use a 6+LLL with Beginner's and intuitive techniques.

I sometimes solve my 3x3 with Corners-first, ZZ, Petrus, Roux, and SBS just for fun.

Everyone sucks at blockbuilding when they first start
 
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