well, you really need to upgrade BOTH mic and soundcard.
but if I had to pick ONE I'd upgrade the MIC first. however, doing that you're likely going to actually cost yourself more in the future than if you upgraded both at the same time.
if you can only afford a MIC and not a soundcard at the same time, then get a shure SM58 (since you're doing vocals) and a cable for it, and an adapter for 1/8" to go into your onboard soundcard.
the SM-58 is a dynamic mic and does not require phantom power. if you use your onboard soundcard you will not have phantom power available, so you MUST get a dynamic mic. there are some cheaper dynamic mics than the SM-58, but you'd have to get something similar.