1) There is no such thing as a 'shmup for newbies'. If you're prepared to stick with the genre, you want to play something that's challenging but not beyond your comprehension, so as you play it you learn.
2) Get ShmupMAME.
http://shmupmame.wordpress.com/download/
3) Get the ROM for Dodonpachi DaiOuJou*.
4) Make savestates of every part that's hard to you. Practice them and figure out why they're hard and more specifically - what you are doing wrong and need to do differently. Refer to a superplay if needed, like
https://www.youtube.com/watch?v=TL3Q6CR-WjM
5) Practice for fun and to get better.
6) When the game stops feeling hard, get a 1CC. Cool!
*No, it doesn't have to be this game. But, whatever shmup you pick, you will eventually have to memorize parts of it or all of it to get consistent, it's not just DoJ, so just bear that in mind.
**By the way, it doesn't matter what you use to play (keyboard, pad, stick, etc) as long as you can either do correct input on it or are willing to grind it until you can. Make sure you can hit diagonals, repeatedly tap a diagonal, sweep from a diagonal to an orthogonal or back on command without slipping, etc.
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