I think the ACLU does a great job, but they aren't as effective as the NRA.
So now it's chicken-and-egg. Is the ACLU better than the NRA, but uninterested? Or are their different tactics and results a product of the different topics they deal with?
edit: as an aside, I'm big on the second amendment but stopped contributing to the NRA precisely because, among other things, they're clearly not big fans of other civil liberties. Their magazines contain (or used to, anyway) a lot of bias against anyone who didn't support a heavily militarized police force, or was against torture for suspected terrorists, etc. It also wasn't clear to me how all the money they solicited was being tracked for efficacy.
The ACLU has a great record on 1 and 4, as do several of the groups they work with. "Restore the Fourth" is fantastic, and you can guess which amendment they care about.
The NRA is strange and uncomfortable to a lot of people, I think. I share your complaint, but they have strong stances on so many different issues that I've met people who object to them for half a dozen different reasons.
When this country was founded, there were no police. Our adversarial justice system was you deciding you were wronged, going and swearing out a warrant in front of a magistrate, and then executing said warrant with the aid of whatever bruisers you could muster. Generally clubs would be preferable to pistols, and there was no chance of using a musket. Also, while there was not an explicit prohibition on maintaining a standing army, the time limit on military appropriations was intended to limit military spending to war-time.
To some degree this changed in 1812, when the far-more-numerous American militia failed to contest the burning of the nation's capital. To some degree it changed in 1847 when Samuel Colt became a successful revolver manufacturer. But to whatever degree this nation has changed its ideas about firearms, these have not been reflected in law, and we've been papering over the situation for the last century at least.
Where the NRA fits into this is to demand protection and expansion of the individual right to bear arms without any consideration whatsoever of the original context of the second amendment. I don't necessarily object to their viewpoint, but their myopia on the subject does make it rather difficult to discuss. Generally I think the way this goes is, ["Founder's intentions", "individual right to bear arms", "standing army"] : pick any two.
"In striking down Washington D.C.'s handgun ban by a 5-4 vote, the Supreme Court's decision in D.C. v. Heller held for the first time that the Second Amendment protects an individual's right to keep and bear arms, whether or not associated with a state militia. The ACLU disagrees with the Supreme Court's conclusion about the nature of the right protected by the Second Amendment. However, particular federal or state laws on licensing, registration, prohibition, or other regulation of the manufacture, shipment, sale, purchase or possession of guns may raise civil liberties questions."
In practice, they don't advocate for Second Amendment protection. That's not necessarily a bad thing, I think it would destroy their effectiveness elsewhere without achieving much, but their acknowledgement of the right hasn't involved them actually getting involved with legal cases so far.