Hi anitract, welcome to RO! Thank you for writing a perfectly well planned and presented question; this is a rarity from people who are starting out.
For this response, I assumed that you already have an audio recording program. If you don;t, you can always use the free and totally decent program Audacity. I also assumed that you don;t want to become a full blown recording engineer; rather, you just want to record some songs.
My opinion is that you should spend as little as possible on the audio interface and preamp and as much as possible on the microphone. The microphone is next in line, after source and room acoustics, in the heirarchy of sound quality. Since you need to keep the cost down in the interface/preamp department, I believe you should combine these two things into one device. There's ony one good choice here that keeps things simple, cheap, and respectably high quality - the M-Audio Mobile Pre USB. $150 and your interface and pres are taken care of. I don't think you can get away any cheaper.
OK, so we have $350 to spen on mics. What? No cables, stands, etc? Fine. $300. Now this is the hard part. There's no inexpensive mic I know of that will record both vocal and acoustic guitar as well as teh Audio Technica 4033, but these (the new 4033/CL) are $400 new. Perhaps yopu could find a used original 4033 for $300 or less. The Studio Projects B1 might be able to do something remotely similar in a pinch, and they are only $100. Teh problem is that acoustic guitars like small diaphragm mics and vocals like large. Also, acoustic guitars like to be recorded in stereo ( i.e., two mics). There are a couple good cheap small diaphragm condensers out there like the Studio Projects C4, but a pair of those would put you over the budget. Also, one small diaphragm mic and one large would probably put you over the budget. You could always go REALLY cheap and buy some Behringer-like crap, but I would'nt if I were you. You will hate them and you will want to buy more mics. You know what they say, buy cheap, buy twice. If I were you, I would porobably spend the $300 on a good large diaphragm vocal condenser, use it on guitar, and save up until I can afford a pair of small diaphragm condensers.
Perhaps someone else who knows budget mics better than I do will be able to come up with another idea. Best of luck.