OK, we are getting somewhere. Now we can begin to narrow down how to go about it. When mic'ing a standup (or console/spinet), the live setup usually involves one or two dynamics close on the soundboard in the back. This works for a live setup, as it places the piano between the vocalist and the piano mic(s), and allows you to close mic the soundboard, so you don't get a lot of bleed from the vocalist to the piano mic(s). This is not the ideal way to do it in the studio.
First, you have to choke down some reality. With only 2 inputs, and wanting to get the detailed sound a studio lives for, the *right* way to do it is to record the piano and the vocals ****separately****. This prevents microphone bleed and allows you to record the piano with 2 mics, which may or may not be a stereo recording. A piano is a big thing, and like the elephant and the blind men, placing microphones in different places yields very different results.
Unfortunately, studio recording is the most expensive of the various scenarios, and your budget is very limited. In a more perfect world, I would choose to mic the piano with 2 small diaphragm condensers, and then the vocals with one large diaphragm condenser. On a $300 budget, we are stretching it to do 2 mics, so I would go with 2 large diaphragm condensers for the piano, and then use one of them for vocals. And- you are really going to need a couple of boom stands and cables, so we can't go much over $100 apiece for the mics.
Furthermore, I am not a fan of most wicked-cheap options, which usually involves Nady or Behringer mics. Although I'm not usually a fan of studio packs, here's one option that gets you pretty damn close to your $300- Two of these-
http://www.8thstreet.com/product.asp?ProductCode=70712&Category=Microphones
That gets you 2 mics with the boom stands, cables, and shock mounts, which are applicable for both piano and vocals, although for vocals, I strongly recommend adding a pop filter, such as-
http://www.8thstreet.com/product.asp?ProductCode=31265&Category=Recording_Accessories
There are less expensive options, such as:
http://www.8thstreet.com/product.asp?ProductCode=30178&Category=Microphones
Frankly, if I was going the Marshall/MXL route, I would prefer a pair of these:
http://www.8thstreet.com/product.asp?ProductCode=6458&Category=Microphones
and buy the stands, cables. shock mounts, and a pop filter separately, but that would put you over budget by a fair amount.
Here's another option, which gets you 2 small diaphragms and one large, with the pop filter and a shock mount for the large diaphragm, by CAD:
http://www.8thstreet.com/product.asp?ProductCode=30526&Category=Microphones
Of course, there are many other options, but those are my best bets. I personally would go with the B1's or the V67's, but I could probably show you a hundred options that would work. How you place these mics depends a lot on your room. I would place the 2 mics overhead with the top open. one on the bass side, and one on the treble side. Basically, the better your room sounds, the farther away from the piano the mics can be.
Once you've settled on some mics and set them up, you can tell us more about your room and what problems you are experiencing, and I can suggest other things to try. Note this, though- There are as many mic decisions on a budget and as many placement configurations as there are people on this board, and a whole lot of people will likely begin to chime in with multiple suggestions, many of which will be just as valid as mine. It *will* get confusing, because there are simply a ton of ways to do it. I have recommended about 3 of the thousands of possible options. Keep the info coming, and I, at least, will be there for you. There is no perfect solution. I've got about $10,000 worth of microphones, and I have only scratched the surface. I don't think you can go horribly wrong with any of the mics I have listed, as they are all perfectly good cheap mics from respected companies that you can resell for a fair fraction of what you paid for them if they don't work out for you.
Note- all the links I have used are from 8th street, which is one of my favorite online outfits to deal with. If you can beat their prices significantly elsewhere, go for it, but they've been pretty good to me over the years. Best of luck.-Richie