Audiobass is right on. The "underpowering" thing is one of the great horrible myths of car audio.
My answer is going to be one that you'll hate, but one that some of you won't be surprised by; that is: it depends.
What shape are your current speakers in?
IF they are in good shape, THEN it might be good to buy the amplifier now if all you're looking for is more distortion free volume.
Why? Because most 4-channel amplifiers have high pass crossovers built in. A quality and correctly set high pass crossover will greatly increase the power handling and sound quality of your stock speakers.
That isn't what I would do first, however. Here's my priority list / guide in car audio budget system design: (assuming nothing factory is broken or complete junk)
1) Subwoofer / Subwoofer Amplifier!
This is the number one best addition you can make right away from a stock system. Why? Because it actually adds frequencies to your stereo that you are unable to hear unless you have it. Most people push their car stereos to distortion / blowing / etc. because their current system doesn't have enough emotion or completeness. So, what do they do? They jack up the bass and they jack up the volume. This is what makes factory systems sound like complete junk. Improper use. By getting a subwoofer you can add the emotion and frequencies WITHOUT abusing your mids. You may say, "subwoofers are only for high school kids," but they aren't. You don't need the 2 12" chrome junk pair from Best Buy to add some bass. A single unflashy woofer in a small box with small power will add quite a bit to a factory system.
Tip: Buy a 4-channel amplifier at this stage. You can bridge 2 of the channels to the subwoofer and use the other 2 for the front stage. Budget system design at its best.
2) Head Unit
Get yourself a good source. A decent head unit, while a poor excuse for an amplifier, can add significant power and clarity to your factory speakers. Most new head units also feature high pass adjustable crossovers. Look for this feature if upgrading in steps. Also look for one with three sets of pre-outs, one for the sub, front, and rear.
3) Front Speakers
Now that you have OK head unit power and won't be abusing the speakers (because the subwoofer will provide the punch), it is finally time for the most important upgrade. Speakers. Plan to spend as much money as possible on the front stage. This is where 90% of your system sound will be shaped. Let your ears guide your pocket when auditioning speakers. Bring your own music. Pay attention to the installation. Get a good seal around the speaker. Make sure the baffle is as solid and leak free as possible.
4) Additional Amplifiers
These should be easy to implement since you have all the other equipment now. Just make sure you have large enough power wire run to the amplifier's location and you're ready to go. My number one piece of advice for amplifiers: if it seems too good to be true, it probably is. Seriously, be suspicious about amplifiers that give way too many watts for the money. Unfortunately, demoing amplifiers is difficult. To some extent you'll need to go off manufacturer reputation. Ask here about amplifier brands folks respect. If professionals respect a brand, the brand probably rates its amplifiers honestly and doesn't have serious reliability issues. Shoot for an amplifier with RMS power anywhere UNDER the RMS power of whatever speaker or subwoofer you plan to drive.
5) Everything else.
New Project: 2003 Pathfinder