I plan on cooking pretty simple foods and will need a knife for things like stir fry, the occasional meat dish, soups, casseroles, basically just standard fare. What brand and type will get me good value and all-purpose use?
I recommend that you get a chef's knife or a santoku (both are general purpose knives), and a paring knife. For most western cooks who will be learning from western examples, the chef's knife may be the better choice.
These two knives will cover most needs. See:
If you were to add a third knife, a serrated bread knife can be very useful for certain tasks (like bread, and perhaps unexpectedly, chopping chocolate).
I have three: a santoku style all-purpose knife, a long bread knife (also good for grating/scraping), and a cleaver since I often buy meat in large chunks.
Brands aren't really important unless they offer something unique that you find desirable, but do spend more than $10 or you'll likely end up with something that won't last. A good knife is one that feels comfortable and has a decent rep. If you can satisfy that, then just like a guitar, it will get better the more you use it.
Also, get a honing steel to keep it in shape.
Just a Chef knife, and a pairing knife. However, make sure that you love working with them. I recommend that you get 2 or three of each, bring them home, and experiment on a potato or cucumber. then return the un-easy ones, and keep your favorite grip friendly ones. good luck.