..... Get a Shure SM57 mic to record the guitar(s.) I think they run about $80 new, but I'm sure you can find a (gently) used one for about 1/2 that. If you're really tight on $, you can probably get away with using the SM57 to record vocals as well - assuming you're not trying to record both the guitar and vox at the same time.
If you've got some money left over after buying your guitar mic, you might consider the Shure SM58 for a vocal mic. While not as common as the SM57, with a little hunting on the web you'll be able to find a used SM58 for around $70.
As far as a filter, I'm not sure what you are referring to, but you don't need anything between the mic and your guitar amp, except for a few inches of space. :-) For vocals, you might want to consider using a "pop" screen. In a pinch you can create a homeade popscreen by putting a thin windscreen or a piece of thin fabric over the mic. Just make sure it's think enough so you don't muffle all the high end in the vocals.
Have fun!