I don`t see the advantages in using phonetic-similar system on keyboards
The advantage is that it takes less to learn.
I think that for non-native the similarity between W/Ш or R/Р or Y/Ы (an so on) makes no sense.
There is not much of “so on” for you sample: d for д, v for в, a for а, o for о and so on totally make sense.
I will wait before buying that app
The one on Russian Phonetic Keyboard: to-print page is a free solution.
eugrus wrote: “There is not much of “so on” for you sample: d for д, v for в, a for а, o for о and so on totally make sense.”
@eugrus: I didn`t know that.
Mike - I’m going to answer your specific questions below. In addition I’ll just say that I started differently than the way you are planning, and leave it at that. You having a good background in Polish and a different mother tongue makes your situation quite different from mine. Because of your abilities, I’m confident that you will develop an excellent learning plan.
I completed the new english based Assimil Russian course (100 lessons). Assimil is an excellent source of graded short native dialogs with accompanying texts. However, Assimil doesn’t “work” for me, meaning that it didn’t take me from zero to B2 by following their method as they promise. I didn’t expect it to do that, but I was hoping for better results. Feeding me grammar little by little this way is probably helpful to a certain extent, but it didn’t make it stick nearly as well as some other courses. But if you are already sold on the methodology, and if it already works for you, the Russian course appears to be well put together.
The first “course” I completed in Russian, Teach Yourself Beginner’s Russian Script, is surprisingly good for teaching one how to read Russian handwriting.
http://www.amazon.com/Teach-Yourself-Beginners-Russian-Script/dp/0071419861/ref=sr_1_2?s=books&ie=UTF8&qid=1386220217&sr=1-2&keywords=russian+script
I bought a keyboard with Russian characters, but admit that I never learned how to touch type. I couldn’t find a good mac tool to teach it, so I just struggled along hunting and picking.
Good luck!
Thank you for your detailed answer and advice.
I don’t think Assimil will take me anywhere close to B2. That is just marketing. I have reached maybe a B1 level in Spanish and Portuguese only, after an Assimil course and without using any other source. However, I find these courses better than any other courses I know. TY are probably better to learn basic structures (I used TY to get started in Bulgarian before spending 3 months in Bulgaria, and I was quite happy with what I learnt) but they are quite boring.
As I said, I have bought other books to use with the Assimil course. I will also look at the TY book you used.
I have already bought the stickers for my keyboard, I will let you know how they work.
I have ordered the “Read and write Russian script” TY book, which is probably a new edition of your book.
I also started learning the beautiful russian language. For typing in on my PC, I’m using a online russian keyboard like http://russtype.com/ . This one has a great UI and you are able to type with your own keyboard and the online keyboard writes it in cyrill 
This website helped me understand the basics of Russian grammar and alphabets:
Getting started learning the Russian language
Write down the Cyrillic alphabets and their English (almost) equivalents on a page and try transliterating anything and everything that comes in your mind. Then do some phonetic research on for a good accent. The ‘soft sign’ and ‘hard sign’ may be a little hurdle in the path. Refer these videos:a) Hard and Soft Consonants in Russian - YouTube b) More on Soft and Hard Signs in Russian - YouTube
3.To type in Russian try this: Try Google Input Tools online – Google Input Tools