At this point, you've probably gone and made it more difficult than it needs to be for yourself. You've probably sat through the explanation of the 4 C's of diamonds: clarity, color, cut and carat weight. If you haven't yet been told about the 4 C's, READ NO FURTHER. Trust your eyes instead.
These two reasons are not as strongly connected as you might think, that is, rarer diamonds do not necessarily look prettier than less rare diamonds. The only thing that directly correlates with the rarity of the stone is its price. You need to decide what makes a diamond valuable to you. The rarity is easy to judge -- rarer stones cost more. The prettiness is also easy to judge -- how does the stone look to you? It only gets tricky when you try to correlate the prettiness of the stone with the 4 C's.
In order of decreasing rarity and price, the clarity scale goes:
Inclusions are anything you can see inside the crystal, be these smaller crystals, carbon specks, small cracks (feathers) or anything else. As far as the prettiness of the stone goes, everything rated SI2 or higher looks the same. SI2 is defined as the clarity grade at which no inclusions are visible to the naked eye. At everything from SI2 on up, the inclusions can only be seen with magnification. Of course, even though the stones still look the same, as you go up the scale in rarity, you also rapidly go up the scale in price.
Color is given an alphabetic rating starting with 'D' for colorless stones and going down the alphabet from there with increasing degrees of color (usually yellow or brown). As you procede down the alphabet, the stones become less rare, and thus go down in price accordingly. As far as how the color rating corresponds to the look of the stone, it is dependent upon how the stone will ultimately be set. If the stone is to be set in platinum or white gold, all color ratings from D to about G will look the same -- no color. If the stone is to be set in yellow gold, all color ratings from D to about I or J will look the same -- the background of the yellow gold will impart some slight color to even the most colorless stone. Below J, the stone will appear visibly yellow or brown tinted to the naked eye. Such stones are sometimes called "champagne diamonds". Just as with clarity though, going down the scale in rarity should mean going down the scale in price.
This refers to the weight of the stone. 200 milligrams equals one carat. Both rarity and price go up sharply with increasing carat weight. This increase is exponential to stone size, thus, a one carat stone will be more rare and hence cost more than 4 quarter carat stones together even though both could be referred to as "one carat total weight". It is best not to worry about carat weight, but to find stones with clarity, color and cut qualities you value and then let your budget determine the carat weight.
Cut refers not to the shape of the stone but to the degree of care the cutter has shown when faceting the raw stone. The quality of the cut affects both how bright the stone looks, and how well it gives you flashes of color when turned in the light. Unlike clarity and color, there is no scale of quantification for cut. Judging cut is easy: does the stone look good to you? If the stone looks bright and sparkly, it has been cut well. If the stone looks either dull or dark, it has been cut poorly. Just look for one which looks good to you. There is not necessarily a correlation between how well cut the stone is, and the stone's price, although stones on which the cutter has been extra careful may command a small premium. Again, my recommendation is to simply trust your eyes and find something that looks pretty. More extensive information on judging the cut of round brilliant diamonds is available, but is not necessary.
The most important thing to remember is that rarity will directly correlate with price, while the actual look of the stone correlates with price only to a limited extent. Once you decide the relative value of the rarity of the stone and the look of the stone, the 4 C's will make more sense to you. Jewelers will typically try to leave you with the impression that the look of the stone is directly correlated to the rarity and hence price of the stone. Don't be fooled; this is simply not true.