I’ve played through most of the Cave iOS versions, as well as Shogun, and liked them, but wouldn’t recommend them as a gateway due to the different control scheme. My favorite of these is Bug Princess, which actually does offer a level-by-level mode with separate leaderboards that I loved (and even got into the top 5 on the leaderboard for the first stage on the highest difficulty). However, all of them have slightly awkward controls for everything but movement, and suffer from being obvious ports, with some ugly scaling issues. I’ve also wound up with quite a few of the indie games brought over by Rockin Katz and Nyu Media through various bundles, but haven’t put a lot of time into them. None of them jump out at me as great gateway recommendation due to a general lack of polish and features (native gamepad support, resolutions/fullscreen mode, etc.), and fairly lackluster theme/art (generic spaceships or generic anime girls). I also took another crack at Ikaruga, which I had bounced off before, and was able to get a little more into it but still didn’t finish.
I do enjoy the genre now, but nothing else has grabbed me quite as hard as Jamestown’s well-presented, tough-but-achievable challenges. One aspect I had forgotten to mention before is the 5-star ranking system for score; having a concrete score target to reach motivated me to replay and learn levels much more effectively than an amorphous “improve your personal high score, with an effectively infinite ceiling”.