the kernel used depends on what hardware you have, if something is not detected or works partially and you think that a new kernel could help, you can install a newer kernel
having a single core cpu has no influence over the kernel you use afik, at least with recent kernels
in your particular case where your cpu is a amd capable of 64 bit, the a64 kernel could make your system a little bit faster, it also works for other cpus but most people just select the .pae kernel to use more than 4 gbs of ram when required
in your hardware you can use 2.6.38.8 bfs or a64, also 3.2.18 bfs or a64, also pae but you say you have only 500 mbs of ram, considerably low amount of ram
keep the older, working kernel and install a couple more kernels, each time you boot a new kernel, it will take a couple minutes to configure and detect things, this is normal, you can install multiple kernels, 5 or 6, maybe more but try less while you run tests
if you see the a64 is good for you and all is ok, system stable then keep it, if not, try another until you see one you can use confortably
i am using on a similar cpu kernel 3.2.18 a64 with good results, in my netbook i'm using 2.6.38.8 a64 for some power management problems with newer kernel