Shmups for people who aren't good at shmups?

[Ikagura]

Radiant Silvergun in Very Easy and Story Mode for grinding.

 

[Yousef]

Embodiment of Scarlet Devil :)
And ikaruga

 

[UnDubious]

I'm like OP, I like shmups but I find them to be the hardest classic genre.
Coryoon on the PC Engine/TG-16 is a really good beginner's shmup. Forgiving without being boring, because there's still a lot of action.
Elemental Master is a great Genesis shmup by Technosoft that's considered quite easy for the genre.
Also, Compile made a good 20 shmups or so, and most of them aren't very hard. A few have been mentioned already, but there are many more. GG Aleste and GG Aleste 2 are both very good and super impressive for Game Gear games.