Advice to people new to the genre:
1. Don't continue
Most of the shooters worth playing weren't made to be console games. Gradius is not an NES game, Ikaruga is not a Dreamcast game. They were made to be arcade games. And yes, believe it or not, every single Japanese arcade game I've seen is both completely clearable with a single credit and at its most enjoyable when played with a single credit. In fact, they often turn into noninteractive explosion clip shows if you use as many credits as you "need." Not to mention the countless games that wreck your score when continuing, the games that prevent you from playing them to their entirety when continuing, the games that introduced continues only later in the International releases and home ports, or the games that prevent you from continuing at all. Before you scoff at the thought of a game like Raiden being more than some vacuum that tries to unfairly kill you every two seconds to earn more cash while you continue into infinity, realize that...
2. These games aren't as hard as you think they are
Seriously. You can get halfway through Espgaluda, at least. I promise. If you follow rule 1 closely for a while, you'll realize that the fastest way to get anywhere at all when it comes to these games (or any other arcade games, for that matter) is to play without continuing. Getting wrecked in stage 2 means that you aren't good enough to beat stage 2 yet. It does not mean that you'll never be good enough to beat stage 2.
3. Playing for score isn't the only way to play these games
I have way more fun with a game when I play for survival. At least, when I'm new to it. And honestly, I can't see any other way making sense. What's the point in jumping into DoDonPachi and quitting whenever you break your chain in stage 2 when you can't even get halfway through the game? Start simply by surviving, first, then only get cocky and mess with scoring in areas that you eventually get comfortable in.
4. Don't assume that "bullet hell" means "hard"
I've seen friends new to arcade games have more trouble with the original Gradius than with Mushihimesama Futari 1.5. Hell, some of these people get bored of Touhou games at their normal difficulty now and have never even seen R-Type stage 4. This doesn't mean that all old games are hard and all new bullet-pumped games are easy. Just don't be stupid and take it on a case by case basis.
5. fuck treasure
Ikaruga is a great game, but insanely unorthodox. Everybody should play it, but nobody should let it mess with their opinion on the entire genre a whole lot. Radiant Silvergun really fucks with rule 3 by making you play for scoring. And Gradius V is cool, but man is it long, with just a little too many slow sections. They're clearly a talented bunch, but don't believe anybody who claims them to be the unquestionable best in the genre. I've seen people try to get into shooters by doing nothing but playing Radiant Silvergun for score, getting turned off, and walking away from the genre entirely. I just Do Not Get It.