Replacing your amp will probably give you clearer sound, and allow you to play your speakers louder, but it probably won't help you get more bass that you're looking for. If you want more bass, but not just too much, then you don't even have to spend alot. More likely, if you are trying to increase the frequency range of your stereo (those lower bass notes) you will still have to get a woofer and a small amp. The reason is that lower bass notes need more air movement to be created. Although you could just replace your amp, you will still only have those 5x7s or 6x8s. Thus the surface area of the cones remain the same; to increase the bass waves, it means that instead of increasing cone area to push air, you're relying on the speaker being able to travel more in and out. However, these speakers really don't have a lot of movement, because they also need to play the midrange notes too. It's difficult for them to play both at once.
IMO, I would recommend just keeping the stock amp, and just buying a tiny amp and a small sub, if you don't want a hassle. You don't need a huge amp, even 100 watts RMS will do. Even the 6.5" SAS would help you out if you wanted just a little augmentation. The addition of the amp that you may buy anyway, coupled with just the extra woofer will make a much larger difference in sound than just replacing the amp the existing stock amp in its place. You might just want to take a look at a powered bazooka tube too, they are often easily auditioned by most car audio places- an amp and sub in one package, or the powered MTX thunderform.
The current amp in the car, is weak in comparison to most aftermarket amps, but can still be better than some aftermarket head unit power sources, *depending* on what brand you purchase and it's RMS power rating.
If you do want to get an extra amp, although most amps need RCA inputs available from aftermarket head unit, some also take speaker level inputs. If you would like an amp that doesn't have speaker level inputs, Audiolink has a product that will convert speaker level inputs into RCA outputs, so there you go!
Good luck!