If you are running a version of Windows 98 me 2000 or xp and have a sound card in your machine and a mic (which plugs into the MIC INPUT on the sound card), you can already, although this is extremely basic and can only support one mic. The voice and the guitar would have to be recorded with the same mic, unless you purchase a mixer that allows pluging in more than one mic. The output of the mixer would be connected to the LINE IN on the sound card. Still, everything must be recorded at once.
You can go to Start button/Programs/accessories/entertainment/sound recorder.
Once there run Sound Recorder, there is a help file that will give you step by step instructions on how to record using your microphone or mixer. This is the most basic entry level setup.
If you desire more quality and control over your recording, there are many options for sound cards, microphones, and music multitrack recording programs availible to choose from that will still keep you under your $300 ceiling. A software program I'm familiar with called POWER TRACKS can be purchased from around $40 to $60. That will allow recording one thing and then you can rewind and record something else right along with it multiple times, erase, and edit the individual recordings before you combine them into one stereo wav file.
There are many options for mixers that will still keep you in your price range, and if you are only going to record maybe 2 or 3 things at the most, I really don`t see a need for an 8 input sound card starting out.
I`d recommend doing a bit of reading here. There is a link on the home page that got you here called SOUND CARD BASICS down near the bottom of the page that will help you out quite a bit. Then read the recording link, and mixers. It is highly educational reading and not so technical that it goes over your head. There is a highly recommended site called ZZSOUNDS.COM where you can view the varieties of equipment and prices used for home recording as well.
There are lots of folks here that can help you along thru the initial stages of learning how to use your equipment and get the best results with it. The "search" is a valuable tool as well. Just click the search button up top and enter the text your interested in and stand back, it will be in there somewhere...
Welcome to the Home Recording BBS community....